Theorem sylg 1750

Description: A syllogism combined with generalization. Inference associated with sylgt 1749. General form of alrimih 1751. (Contributed by BJ, 4-Oct-2019.)

Hypotheses

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

Assertion

Ref	Expression
sylg	|- ( ph -> A. x ch )

Proof of Theorem sylg

Step	Hyp	Ref	Expression
1		sylg.1	. 2 |- ( ph -> A. x ps )
2		sylg.2	. . 3 |- ( ps -> ch )
3	2	alimi 1739	. 2 |- ( A. x ps -> A. x ch )
4	1, 3	syl 17	1 |- ( ph -> A. x ch )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1722  ax-4 1737

This theorem is referenced by:  alrimih  1751  aev2  1986  trint  4768  ssrel  5207  kmlem1  8972  bnj1476  30917  bnj1533  30922  bj-ax12ig  32615  axc11n11  32672  bj-modalbe  32678  bj-ax9-2  32891