Theorem 3adantr1

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

	Ref	Expression
Hypothesis	3adantr.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
Assertion	3adantr1	|- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )

Proof

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