Theorem ad2ant2l

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	ad2ant2l	$$⊢\left(\left(\theta \wedge \phi \right)\wedge \left(\tau \wedge \psi \right)\right)\to \chi$$

Proof

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