"for implication" is correct and can be used in written English.
For example, "I believe that the speaker left out certain details for implication."
Eventually she conceded: "I am in the wrong … I unreservedly apologise for implication".
Table 3 gives the projection table for implication.
They can be obtained immediately from Gentzen's sequent-rules for implication.
This is a clear instance of the clause for implication in the Proof Interpretation.
We can model situated inference using a relation I (for "implication").
where ⊃ ̇ is an operator used for reified propositions to mimic the logical operator for implication, ⊃.
Thus we can conclude that for implicational logic (and, in fact, for implication-conjunction logic), Prawitz's completeness conjecture is correct, i.e., conjunction-implication logic is complete with respect to validity-based semantics.
This is one of those years for implications.
Consider, for instance, implication.
Our findings are useful for policy implications.
The implication for today?
