deduction theorem

The deduction theorem in logic shows that if assuming a statement \( P \) leads to another statement \( Q \), then you can conclude that "if \( P \), then \( Q \)" is true overall. In other words, it connects reasoning with or without assuming something. If adding a premise \( P \) helps prove \( Q \), then we can state that \( P \) implies \( Q \) without needing to assume \( P \). This principle helps simplify complex logical arguments by translating assumptions into implications.