Theorem ad2antlr

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999) (Proof shortened by Wolf Lammen, 20-Nov-2012)

	Ref	Expression
Hypothesis	ad2ant.1	$$⊢\phi \to \psi$$
Assertion	ad2antlr	$$⊢\left(\left(\chi \wedge \phi \right)\wedge \theta \right)\to \psi$$

Proof

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