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The use of variable functors with liberal substitution enables a number of principles of propositional logic to be given startlingly compressed and elegant formulations, for example the principle of bivalence in the form which can be read as "if something is true of a false proposition then if it true of a true proposition, it is true of any proposition" (C00 is a true proposition).
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A sentence is true if and only if it is true in every admissible structure.
One wonders if it's true.
She wondered if it was true.
If it's true, poor guy.
Babette asked if it was true.
"If it's true!" cautioned his colleague.
If it's true – great.
But if it is true?
Even if it is true".
And if it's true......
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