Theorem 3adant1l

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Hypothesis	ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	3adant1l	$$⊢\left(\left(\tau \wedge \phi \right)\wedge \psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2		simpr	$$⊢\left(\tau \wedge \phi \right)\to \phi$$
3	2 1	syl3an1	$$⊢\left(\left(\tau \wedge \phi \right)\wedge \psi \wedge \chi \right)\to \theta$$