Theorem adantrl

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 24-Nov-2012)

	Ref	Expression
Hypothesis	adant2.1	|- ( ( ph /\ ps ) -> ch )
Assertion	adantrl	|- ( ( ph /\ ( th /\ ps ) ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		adant2.1	|- ( ( ph /\ ps ) -> ch )
2		simpr	|- ( ( th /\ ps ) -> ps )
3	2 1	sylan2	|- ( ( ph /\ ( th /\ ps ) ) -> ch )