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Metamath Proof Explorer

Theorem bicomi

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

		Ref	Expression
	Hypothesis	bicomi.1	$⊢ φ \leftrightarrow ψ$
	Assertion	bicomi	$⊢ ψ \leftrightarrow φ$

Step	Hyp	Ref	Expression
1		bicomi.1	$⊢ φ \leftrightarrow ψ$
2		bicom1	$⊢ (φ \leftrightarrow ψ) \to (ψ \leftrightarrow φ)$
3	1 2	ax-mp	$⊢ ψ \leftrightarrow φ$