Theorem ad4ant123

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

	Ref	Expression
Hypothesis	ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	ad4ant123	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\wedge \tau \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2	1	3expa	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	2	adantr	$$⊢\left(\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\wedge \tau \right)\to \theta$$