Theorem ad2ant2r

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 8-Jan-2006)

	Ref	Expression
Hypothesis	ad2ant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	ad2ant2r	$$⊢\left(\left(\phi \wedge \theta \right)\wedge \left(\psi \wedge \tau \right)\right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		ad2ant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2	1	adantrr	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \right)\right)\to \chi$$
3	2	adantlr	$$⊢\left(\left(\phi \wedge \theta \right)\wedge \left(\psi \wedge \tau \right)\right)\to \chi$$