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Metamath Proof Explorer

Theorem con1bid

Description: A contraposition deduction. (Contributed by NM, 9-Oct-1999)

		Ref	Expression
	Hypothesis	con1bid.1	$⊢ φ \to (\neg ψ \leftrightarrow χ)$
	Assertion	con1bid	$⊢ φ \to (\neg χ \leftrightarrow ψ)$

Step	Hyp	Ref	Expression
1		con1bid.1	$⊢ φ \to (\neg ψ \leftrightarrow χ)$
2	1	bicomd	$⊢ φ \to (χ \leftrightarrow \neg ψ)$
3	2	con2bid	$⊢ φ \to (ψ \leftrightarrow \neg χ)$
4	3	bicomd	$⊢ φ \to (\neg χ \leftrightarrow ψ)$