Theorem 3adantr3

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

	Ref	Expression
Hypothesis	3adantr.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
Assertion	3adantr3	|- ( ( ph /\ ( ps /\ ch /\ ta ) ) -> th )

Proof

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