| arrow-intro | Given a sentence (at line n), conclude a conditional having it as the consequent and whose antecedent appears in the proof as an assumption (at line m). |
| Annotation: n →I (m) | |
| Assumption set: Everything in the assumption set at line n except m, the line number where the antecedent was assumed. | |
| Comment: The antecedent must be present in the proof as an assumption. We speak of DISCHARGING this assumption when applying this rule. Placing the number m in parentheses indicates it is the discharged assumption. | |
| Also known as: Conditional Proof (CP). | |
| Examples. | |
| (a) | |
1 (1) ~P v Q A | |
2 (2) P A | |
1,2 (3) Q 1,2 vE | |
1 (4) P→Q 3 →I (2) | |
| (b) | |
1 (1) P A | |
2 (2) R A | |
2 (3) P→R 2 →I (1) |