Theorem adantrrl

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

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

Proof

Step	Hyp	Ref	Expression
1		adantr2.1	|- ( ( ph /\ ( ps /\ ch ) ) -> th )
2		simpr	|- ( ( ta /\ ch ) -> ch )
3	2 1	sylanr2	|- ( ( ph /\ ( ps /\ ( ta /\ ch ) ) ) -> th )