Theorem 3adantr2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

	Ref	Expression
Hypothesis	3adantr.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
Assertion	3adantr2	|- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

Proof

Step	Hyp	Ref	Expression
1		3adantr.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
2		3simpb	|- ( ( ps /\ ta /\ ch ) -> ( ps /\ ch ) )
3	2 1	sylan2	|- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )