Theorem adantlll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 2-Dec-2012)

	Ref	Expression
Hypothesis	adantl2.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
Assertion	adantlll	|- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )

Proof

Step	Hyp	Ref	Expression
1		adantl2.1	|- ( ( ( ph /\ ps ) /\ ch ) -> th )
2		simpr	|- ( ( ta /\ ph ) -> ph )
3	2 1	sylanl1	|- ( ( ( ( ta /\ ph ) /\ ps ) /\ ch ) -> th )