Theorem pm5.35 869

Description: Theorem *5.35 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.35	⊢ (((φ → ψ) ∧ (φ → χ)) → (φ → (ψ ↔ χ)))

Proof of Theorem pm5.35

Step	Hyp	Ref	Expression
1		pm5.1 830	. 2 ⊢ (((φ → ψ) ∧ (φ → χ)) → ((φ → ψ) ↔ (φ → χ)))
2	1	pm5.74rd 239	1 ⊢ (((φ → ψ) ∧ (φ → χ)) → (φ → (ψ ↔ χ)))

Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358

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  df-an 360

This theorem is referenced by: (None)