Theorem sylg

Description: A syllogism combined with generalization. Inference associated with sylgt . General form of alrimih . (Contributed by BJ, 4-Oct-2019)

	Ref	Expression
Hypotheses	sylg.1	|- ( ph -> A. x ps )
	sylg.2	|- ( ps -> ch )
Assertion	sylg	|- ( ph -> A. x ch )

Proof

Step	Hyp	Ref	Expression
1		sylg.1	|- ( ph -> A. x ps )
2		sylg.2	|- ( ps -> ch )
3	2	alimi	|- ( A. x ps -> A. x ch )
4	1 3	syl	|- ( ph -> A. x ch )