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Metamath Proof Explorer

Theorem pm5.24

Description: Theorem *5.24 of WhiteheadRussell p. 124. (Contributed by NM, 3-Jan-2005)

		Ref	Expression
	Assertion	pm5.24	$⊢ \neg ((φ \land ψ) \lor (\neg φ \land \neg ψ)) \leftrightarrow ((φ \land \neg ψ) \lor (ψ \land \neg φ))$

Step	Hyp	Ref	Expression
1		xor	$⊢ \neg (φ \leftrightarrow ψ) \leftrightarrow ((φ \land \neg ψ) \lor (ψ \land \neg φ))$
2		dfbi3	$⊢ (φ \leftrightarrow ψ) \leftrightarrow ((φ \land ψ) \lor (\neg φ \land \neg ψ))$
3	1 2	xchnxbi	$⊢ \neg ((φ \land ψ) \lor (\neg φ \land \neg ψ)) \leftrightarrow ((φ \land \neg ψ) \lor (ψ \land \neg φ))$