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Metamath Proof Explorer

Theorem intnanrd

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005)

		Ref	Expression
	Hypothesis	intnand.1	$⊢ φ \to \neg ψ$
	Assertion	intnanrd	$⊢ φ \to \neg (ψ \land χ)$

Step	Hyp	Ref	Expression
1		intnand.1	$⊢ φ \to \neg ψ$
2		simpl	$⊢ (ψ \land χ) \to ψ$
3	1 2	nsyl	$⊢ φ \to \neg (ψ \land χ)$