Theorem 3ad2antr3

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 30-Dec-2007)

	Ref	Expression
Hypothesis	3ad2antl.1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
Assertion	3ad2antr3	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \wedge \chi \right)\right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		3ad2antl.1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
2	1	adantrl	$$⊢\left(\phi \wedge \left(\tau \wedge \chi \right)\right)\to \theta$$
3	2	3adantr1	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \wedge \chi \right)\right)\to \theta$$