Theorem bj-ala1i

Description: Add an antecedent in a universally quantified formula. Inference associated with ala1 . (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Hypothesis	bj-ala1i.1	|- A. x ph
Assertion	bj-ala1i	|- A. x ( ps -> ph )

Proof

Step	Hyp	Ref	Expression
1		bj-ala1i.1	|- A. x ph
2		ala1	|- ( A. x ph -> A. x ( ps -> ph ) )
3	1 2	ax-mp	|- A. x ( ps -> ph )