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	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	3adant2r	|- ( ( ph /\ ( ps /\ ta ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	|- ( ( ph /\ ps /\ ch ) -> th )
2		simpl	|- ( ( ps /\ ta ) -> ps )
3	2 1	syl3an2	|- ( ( ph /\ ( ps /\ ta ) /\ ch ) -> th )