Theorem bicomi

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

	Ref	Expression
Hypothesis	bicomi.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	bicomi	$$⊢\psi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		bicomi.1	$$⊢\phi \leftrightarrow \psi$$
2		bicom1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \leftrightarrow \phi \right)$$
3	1 2	ax-mp	$$⊢\psi \leftrightarrow \phi$$