Theorem 3adant3r2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008)

	Ref	Expression
Hypothesis	ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	3adant3r2	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \wedge \chi \right)\right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3expb	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
3	2	3adantr2	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \wedge \chi \right)\right)\to \theta$$