Theorem 3adant3

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Hypothesis	3adant.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	3adant3	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \chi$$

Proof

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