Theorem pm3.45 807

Description: Theorem *3.45 (Fact) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.45	⊢ ((φ → ψ) → ((φ ∧ χ) → (ψ ∧ χ)))

Proof of Theorem pm3.45

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ((φ → ψ) → (φ → ψ))
2	1	anim1d 547	1 ⊢ ((φ → ψ) → ((φ ∧ χ) → (ψ ∧ χ)))

Syntax hints:   → wi 4   ∧ 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:  rabss2  3350