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Metamath Proof Explorer

Theorem con4bii

Description: A contraposition inference. (Contributed by NM, 21-May-1994)

		Ref	Expression
	Hypothesis	con4bii.1	$⊢ \neg φ \leftrightarrow \neg ψ$
	Assertion	con4bii	$⊢ φ \leftrightarrow ψ$

Step	Hyp	Ref	Expression
1		con4bii.1	$⊢ \neg φ \leftrightarrow \neg ψ$
2		notbi	$⊢ (φ \leftrightarrow ψ) \leftrightarrow (\neg φ \leftrightarrow \neg ψ)$
3	1 2	mpbir	$⊢ φ \leftrightarrow ψ$