Theorem biancomi

Description: Commuting conjunction in a biconditional. (Contributed by Peter Mazsa, 17-Jun-2018)

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

Proof

Step	Hyp	Ref	Expression
1		biancomi.1	⊢ ( 𝜑 ↔ ( 𝜒 ∧ 𝜓 ) )
2		ancom	⊢ ( ( 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ) )
3	1 2	bitr4i	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )