Theorem intnanrd

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

	Ref	Expression
Hypothesis	intnand.1	$$⊢\phi \to \neg \psi$$
Assertion	intnanrd	$$⊢\phi \to \neg \left(\psi \wedge \chi \right)$$

Proof

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