Description: Importation inference from a logical equivalence. (Contributed by NM, 3-May-1994)
Ref | Expression | ||
---|---|---|---|
Hypothesis | biimpa.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
Assertion | biimpar | ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimpa.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
2 | 1 | biimprd | ⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) ) |
3 | 2 | imp | ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 ) |