Description: Infer implication from disjunction. (Contributed by NM, 11-Jun-1994)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ori.1 | ⊢ ( 𝜑 ∨ 𝜓 ) | |
Assertion | ori | ⊢ ( ¬ 𝜑 → 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ori.1 | ⊢ ( 𝜑 ∨ 𝜓 ) | |
2 | df-or | ⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( ¬ 𝜑 → 𝜓 ) ) | |
3 | 1 2 | mpbi | ⊢ ( ¬ 𝜑 → 𝜓 ) |