Theorem anbi2ci

Description: Variant of anbi2i with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011)

	Ref	Expression
Hypothesis	anbi.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	anbi2ci	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		anbi.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	anbi1i	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ) )
3	2	biancomi	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ) )