Theorem pm2.61ddan

Description: Elimination of two antecedents. (Contributed by NM, 9-Jul-2013)

	Ref	Expression
Hypotheses	pm2.61ddan.1	$$⊢\left(\phi \wedge \psi \right)\to \theta$$
	pm2.61ddan.2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
	pm2.61ddan.3	$$⊢\left(\phi \wedge \left(\neg \psi \wedge \neg \chi \right)\right)\to \theta$$
Assertion	pm2.61ddan	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		pm2.61ddan.1	$$⊢\left(\phi \wedge \psi \right)\to \theta$$
2		pm2.61ddan.2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
3		pm2.61ddan.3	$$⊢\left(\phi \wedge \left(\neg \psi \wedge \neg \chi \right)\right)\to \theta$$
4	2	adantlr	$$⊢\left(\left(\phi \wedge \neg \psi \right)\wedge \chi \right)\to \theta$$
5	3	anassrs	$$⊢\left(\left(\phi \wedge \neg \psi \right)\wedge \neg \chi \right)\to \theta$$
6	4 5	pm2.61dan	$$⊢\left(\phi \wedge \neg \psi \right)\to \theta$$
7	1 6	pm2.61dan	$$⊢\phi \to \theta$$