Theorem pm5.31 571

Description: Theorem *5.31 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.31	⊢ ((χ ∧ (φ → ψ)) → (φ → (ψ ∧ χ)))

Proof of Theorem pm5.31

Step	Hyp	Ref	Expression
1		pm3.21 435	. . 3 ⊢ (χ → (ψ → (ψ ∧ χ)))
2	1	imim2d 48	. 2 ⊢ (χ → ((φ → ψ) → (φ → (ψ ∧ χ))))
3	2	imp 418	1 ⊢ ((χ ∧ (φ → ψ)) → (φ → (ψ ∧ χ)))

This proof depends on syntax axioms:   → wi 4   ∧ 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: (None)