Theorem pm5.31r 832

Description: Variant of pm5.31 831. (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		ax-1 6	. 2 ⊢ (𝜒 → (𝜑 → 𝜒))
2		id 22	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
3	1, 2	anim12ii 621	1 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜒 ∧ 𝜓)))

Syntax hints:   → wi 4   ∧ wa 399

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 210  df-an 400

This theorem is referenced by:  2reuimp  44467