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### Explanation of implication-introduction rule

Every assumption that is introduced between brackets has to be discharged at some point for the proof to be complete. Otherwise, we could prove that $A$ is true for any given $A$ as follows. ...
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### Explanation of implication-introduction rule

I recommend Mario Román's answer, particularly the connection to the lambda calculus, but I'll add a third perspective. I dislike the natural deduction notation, but I do like the natural deduction ...
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