Theorem 3adant2r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 25-Jun-2022)

	Ref	Expression
Hypothesis	ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	3adant2r	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \right)\wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
2		simpl	$$⊢\left(\psi \wedge \tau \right)\to \psi$$
3	2 1	syl3an2	$$⊢\left(\phi \wedge \left(\psi \wedge \tau \right)\wedge \chi \right)\to \theta$$