Theorem bicomi

Description: Inference from commutative law for logical equivalence. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypothesis	bicomi.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	bicomi	⊢ ( 𝜓 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bicomi.1	⊢ ( 𝜑 ↔ 𝜓 )
2		bicom1	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) )
3	1 2	ax-mp	⊢ ( 𝜓 ↔ 𝜑 )