Theorem pm5.31 827

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		simpr 484	. 2 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → 𝜓))
2		simpl 482	. 2 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → 𝜒)
3	1, 2	jctird 526	1 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜓 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  bj-bary1lem1  35409