Theorem anim12ci 550

Description: Variant of anim12i 549 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypotheses

Ref	Expression
anim12i.1	⊢ (φ → ψ)
anim12i.2	⊢ (χ → θ)

Assertion

Ref	Expression
anim12ci	⊢ ((φ ∧ χ) → (θ ∧ ψ))

Proof of Theorem anim12ci

Step	Hyp	Ref	Expression
1		anim12i.2	. . 3 ⊢ (χ → θ)
2		anim12i.1	. . 3 ⊢ (φ → ψ)
3	1, 2	anim12i 549	. 2 ⊢ ((χ ∧ φ) → (θ ∧ ψ))
4	3	ancoms 439	1 ⊢ ((φ ∧ χ) → (θ ∧ ψ))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  2exeu  2281  frecxp  6315