Theorem 3ad2antl2

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007)

	Ref	Expression
Hypothesis	3ad2antl.1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
Assertion	3ad2antl2	$$⊢\left(\left(\psi \wedge \phi \wedge \tau \right)\wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3ad2antl.1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
2	1	adantlr	$$⊢\left(\left(\phi \wedge \tau \right)\wedge \chi \right)\to \theta$$
3	2	3adantl1	$$⊢\left(\left(\psi \wedge \phi \wedge \tau \right)\wedge \chi \right)\to \theta$$