Theorem pm5.31 346

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		pm3.21 262	. . 3 ⊢ (𝜒 → (𝜓 → (𝜓 ∧ 𝜒)))
2	1	imim2d 54	. 2 ⊢ (𝜒 → ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜒))))
3	2	imp 123	1 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜓 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by: (None)