Theorem negel

Description: An inference for negation elimination. (Contributed by Giovanni Mascellani, 24-May-2019)

	Ref	Expression
Hypotheses	negel.1	$$⊢\psi \to \chi$$
	negel.2	$$⊢\phi \to \neg \chi$$
Assertion	negel	$$⊢\left(\phi \wedge \psi \right)\to \perp$$

Proof

Step	Hyp	Ref	Expression
1		negel.1	$$⊢\psi \to \chi$$
2		negel.2	$$⊢\phi \to \neg \chi$$
3	1	adantl	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
4	2	adantr	$$⊢\left(\phi \wedge \psi \right)\to \neg \chi$$
5	3 4	pm2.21fal	$$⊢\left(\phi \wedge \psi \right)\to \perp$$