Theorem anbi1ci

Description: Variant of anbi1i with commutation. (Contributed by Peter Mazsa, 7-Mar-2020)

	Ref	Expression
Hypothesis	anbi.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	anbi1ci	⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		anbi.1	⊢ ( 𝜑 ↔ 𝜓 )
2	1	anbi2i	⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜒 ∧ 𝜓 ) )
3	2	biancomi	⊢ ( ( 𝜒 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜒 ) )