Theorem ad2antll

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 19-Oct-1999)

	Ref	Expression
Hypothesis	ad2ant.1	$$⊢\phi \to \psi$$
Assertion	ad2antll	$$⊢\left(\chi \wedge \left(\theta \wedge \phi \right)\right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	$$⊢\phi \to \psi$$
2	1	adantl	$$⊢\left(\theta \wedge \phi \right)\to \psi$$
3	2	adantl	$$⊢\left(\chi \wedge \left(\theta \wedge \phi \right)\right)\to \psi$$