Theorem 3ad2ant2

Description: Deduction adding conjuncts to an antecedent. (Contributed by NM, 21-Apr-2005)

	Ref	Expression
Hypothesis	3ad2ant.1	$$⊢\phi \to \chi$$
Assertion	3ad2ant2	$$⊢\left(\psi \wedge \phi \wedge \theta \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		3ad2ant.1	$$⊢\phi \to \chi$$
2	1	adantr	$$⊢\left(\phi \wedge \theta \right)\to \chi$$
3	2	3adant1	$$⊢\left(\psi \wedge \phi \wedge \theta \right)\to \chi$$