Theorem intn3an1d

Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007) (Proof shortened by Andrew Salmon, 26-Jun-2011)

	Ref	Expression
Hypothesis	intn3and.1	$$⊢\phi \to \neg \psi$$
Assertion	intn3an1d	$$⊢\phi \to \neg \left(\psi \wedge \chi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		intn3and.1	$$⊢\phi \to \neg \psi$$
2		simp1	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \psi$$
3	1 2	nsyl	$$⊢\phi \to \neg \left(\psi \wedge \chi \wedge \theta \right)$$