Theorem ad4ant13

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)

	Ref	Expression
Hypothesis	ad4ant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	ad4ant13	$$⊢\left(\left(\left(\phi \wedge \theta \right)\wedge \psi \right)\wedge \tau \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		ad4ant2.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2	1	adantr	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \tau \right)\to \chi$$
3	2	adantllr	$$⊢\left(\left(\left(\phi \wedge \theta \right)\wedge \psi \right)\wedge \tau \right)\to \chi$$