Theorem adantld

Description: Deduction adding a conjunct to the left of an antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 20-Dec-2012)

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

Proof

Step	Hyp	Ref	Expression
1		adantld.1	|- ( ph -> ( ps -> ch ) )
2		simpr	|- ( ( th /\ ps ) -> ps )
3	2 1	syl5	|- ( ph -> ( ( th /\ ps ) -> ch ) )