Theorem pm5.74ri

Description: Distribution of implication over biconditional (reverse inference form). (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Hypothesis	pm5.74ri.1	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) )
Assertion	pm5.74ri	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.74ri.1	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) )
2		pm5.74	⊢ ( ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) ↔ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → 𝜒 ) ) )
3	1 2	mpbir	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )