Theorem anim12ci

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

	Ref	Expression
Hypotheses	anim12i.1	⊢ ( 𝜑 → 𝜓 )
	anim12i.2	⊢ ( 𝜒 → 𝜃 )
Assertion	anim12ci	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜃 ∧ 𝜓 ) )

Proof

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