Theorem anim12ci 322

Description: Variant of anim12i 321 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 321	. 2 ⊢ ((χ ∧ φ) → (θ ∧ ψ))
4	3	ancoms 255	1 ⊢ ((φ ∧ χ) → (θ ∧ ψ))

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem is referenced by:  dfco2a  4764  funco  4883  fliftval  5383  ltsrprg  6675  difelfznle  8763