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Metamath Proof Explorer

Theorem pm4.15

Description: Theorem *4.15 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 18-Nov-2012)

		Ref	Expression
	Assertion	pm4.15	$⊢ ((φ \land ψ) \to \neg χ) \leftrightarrow ((ψ \land χ) \to \neg φ)$

Step	Hyp	Ref	Expression
1		con2b	$⊢ ((ψ \land χ) \to \neg φ) \leftrightarrow (φ \to \neg (ψ \land χ))$
2		nan	$⊢ (φ \to \neg (ψ \land χ)) \leftrightarrow ((φ \land ψ) \to \neg χ)$
3	1 2	bitr2i	$⊢ ((φ \land ψ) \to \neg χ) \leftrightarrow ((ψ \land χ) \to \neg φ)$