Theorem pm5.31r 33159

Description: Variant of pm5.31 610. (Contributed by Rodolfo Medina, 15-Oct-2010.)

Assertion

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

Proof of Theorem pm5.31r

Step	Hyp	Ref	Expression
1		pm3.2 462	. . 3 ⊢ (𝜒 → (𝜓 → (𝜒 ∧ 𝜓)))
2	1	imim2d 55	. 2 ⊢ (𝜒 → ((𝜑 → 𝜓) → (𝜑 → (𝜒 ∧ 𝜓))))
3	2	imp 444	1 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜒 ∧ 𝜓)))

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by: (None)