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Metamath Proof Explorer

Theorem con4bid

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

		Ref	Expression
	Hypothesis	con4bid.1	$⊢ φ \to (\neg ψ \leftrightarrow \neg χ)$
	Assertion	con4bid	$⊢ φ \to (ψ \leftrightarrow χ)$

Step	Hyp	Ref	Expression
1		con4bid.1	$⊢ φ \to (\neg ψ \leftrightarrow \neg χ)$
2	1	biimprd	$⊢ φ \to (\neg χ \to \neg ψ)$
3	2	con4d	$⊢ φ \to (ψ \to χ)$
4	1	biimpd	$⊢ φ \to (\neg ψ \to \neg χ)$
5	3 4	impcon4bid	$⊢ φ \to (ψ \leftrightarrow χ)$