Theorem ad4ant234

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	ad4ant234	$$⊢\left(\left(\left(\tau \wedge \phi \right)\wedge \psi \right)\wedge \chi \right)\to \theta$$

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	adantlll	$$⊢\left(\left(\left(\tau \wedge \phi \right)\wedge \psi \right)\wedge \chi \right)\to \theta$$