Theorem bj-alexim 32605

Description: Closed form of aleximi 1759 (with a shorter proof, so aleximi 1759 could be deduced from it -- exim 1761 would have to be proved first, but its proof is shorter (currently almost a subproof of aleximi 1759)). (Contributed by BJ, 8-Nov-2021.)

Assertion

Ref	Expression
bj-alexim	|- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( E. x ps -> E. x ch ) ) )

Proof of Theorem bj-alexim

Step	Hyp	Ref	Expression
1		alim 1738	. 2 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> A. x ( ps -> ch ) ) )
2		exim 1761	. 2 |- ( A. x ( ps -> ch ) -> ( E. x ps -> E. x ch ) )
3	1, 2	syl6 35	1 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( E. x ps -> E. x ch ) ) )

Syntax hints:   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bj-exalim  32611