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Metamath Proof Explorer

Theorem xorneg

Description: The connector \/_ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016)

		Ref	Expression
	Assertion	xorneg	$⊢ (\neg φ ⊻ \neg ψ) \leftrightarrow (φ ⊻ ψ)$

Step	Hyp	Ref	Expression
1		xorneg1	$⊢ (\neg φ ⊻ \neg ψ) \leftrightarrow \neg (φ ⊻ \neg ψ)$
2		xorneg2	$⊢ (φ ⊻ \neg ψ) \leftrightarrow \neg (φ ⊻ ψ)$
3	2	con2bii	$⊢ (φ ⊻ ψ) \leftrightarrow \neg (φ ⊻ \neg ψ)$
4	1 3	bitr4i	$⊢ (\neg φ ⊻ \neg ψ) \leftrightarrow (φ ⊻ ψ)$