Theorem pm5.74ri 237

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

Hypothesis

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

Assertion

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

Proof of Theorem pm5.74ri

Step	Hyp	Ref	Expression
1		pm5.74ri.1	. 2 ⊢ ((φ → ψ) ↔ (φ → χ))
2		pm5.74 235	. 2 ⊢ ((φ → (ψ ↔ χ)) ↔ ((φ → ψ) ↔ (φ → χ)))
3	1, 2	mpbir 200	1 ⊢ (φ → (ψ ↔ χ))

Syntax hints:   → wi 4   ↔ wb 176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  bitrd  244  bibi2d  309  tbt  333  sbco2d  2087  2mos  2283