Theorem pm5.74ri 445

Description: Distribution of implication over biconditional (reverse inference rule).

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		pm5.74 442	. 2 ⊢ ((φ → (ψ ↔ χ)) ↔ ((φ → ψ) ↔ (φ → χ)))
3	1, 2	mpbir 165	1 ⊢ (φ → (ψ ↔ χ))

Syntax hints:   → wi 2   ↔ wb 127

This theorem is referenced by:  iba 486  ibar 487  pm5.1 501  sbco2d 914  cbvald 977  nn0ltp1let 4556

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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