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The expression 'φx' thus contains two variables and stands for a proposition, in particular, the result of applying the function φ to the individual x. is a fundamental axiom of the quantificational theory of PM.
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E.g. "p ⊃ q" stands for any proposition of a certain type.
I do not believe that Théberge v. Galerie d'Art du Petit Champlain inc., 2002 SCC 34 (CanLII), 2 S.C.R. 336, 2002 SCC 34, stands for such a proposition.
But our Constitution has always stood for a different proposition – that we are a nation of laws, not men (and women).
The apparent noun phrase such as 瓜田李下 kua 1 tien 5 li 2 ha 7 in the melon plots and under the plum tree, a juxtaposition of two noun phrases, as in 9, may stand for a whole proposition when the missing predicate is restored.
Passed by a Democratic U.S. Congress and signed by a Republican President, the "OSH Act" as it is known, stood for a radical proposition: workers should not have to choose between their livelihoods and their lives.
Gates's nomination unquestionably stands for one proposition: a long-awaited recognition that the administration's war in Iraq has been a disaster.
But the implied proposition, 'P is true' (where P is the name of 'Every proposition is false'), is false because its constituent terms, 'Every proposition is false' and 'true', do not stand for the same thing, since ex hypothesi, P stands for the antecedent proposition 'Every proposition is false', not for things that are true.
37 I think it is fair to say that Cardinal stands for the proposition that a breach of the rules of natural justice or procedural fairness cannot be overlooked on the basis that the reviewing court or appellate tribunal is of the view the result would have been the same had no breach occurred.
7 It may be that Sullivan also stands for the proposition that an individual may not refuse, on Fifth Amendment grounds, to file a return disclosing his name and address, and by implication disclosing that he has earned some income during the previous year.
The last case, Gardner v. New Jersey, 329 U.S. 565 (1947), which held that a bankruptcy court can entertain a trustees objections to a claim filed by a State, stands for the unremarkable proposition that a State waives its sovereign immunity by voluntarily invoking the jurisdiction of the federal courts.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com