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Metamath Proof Explorer

Theorem con2bid

Description: A contraposition deduction. (Contributed by NM, 15-Apr-1995)

		Ref	Expression
	Hypothesis	con2bid.1	$⊢ φ \to (ψ \leftrightarrow \neg χ)$
	Assertion	con2bid	$⊢ φ \to (χ \leftrightarrow \neg ψ)$

Step	Hyp	Ref	Expression
1		con2bid.1	$⊢ φ \to (ψ \leftrightarrow \neg χ)$
2		con2bi	$⊢ (χ \leftrightarrow \neg ψ) \leftrightarrow (ψ \leftrightarrow \neg χ)$
3	1 2	sylibr	$⊢ φ \to (χ \leftrightarrow \neg ψ)$