Theorem 3adant3r1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008)

	Ref	Expression
Hypothesis	ad4ant3.1	|- ( ( ph /\ ps /\ ch ) -> th )
Assertion	3adant3r1	|- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	|- ( ( ph /\ ps /\ ch ) -> th )
2	1	3expb	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
3	2	3adantr1	|- ( ( ph /\ ( ta /\ ps /\ ch ) ) -> th )