Theorem anbi12ci

Description: Variant of anbi12i with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypotheses	anbi12.1	⊢ ( 𝜑 ↔ 𝜓 )
	anbi12.2	⊢ ( 𝜒 ↔ 𝜃 )
Assertion	anbi12ci	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜃 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		anbi12.1	⊢ ( 𝜑 ↔ 𝜓 )
2		anbi12.2	⊢ ( 𝜒 ↔ 𝜃 )
3	1 2	anbi12i	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜃 ) )
4	3	biancomi	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜃 ∧ 𝜓 ) )