Theorem pm5.44 877

Description: Theorem *5.44 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.44	⊢ ((φ → ψ) → ((φ → χ) ↔ (φ → (ψ ∧ χ))))

Proof of Theorem pm5.44

Step	Hyp	Ref	Expression
1		jcab 833	. 2 ⊢ ((φ → (ψ ∧ χ)) ↔ ((φ → ψ) ∧ (φ → χ)))
2	1	baibr 872	1 ⊢ ((φ → ψ) → ((φ → χ) ↔ (φ → (ψ ∧ χ))))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  reldisj  3595