Theorem bj-exlimh 32602

Description: Closed form of close to exlimih 2148. (Contributed by BJ, 2-May-2019.)

Assertion

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

Proof of Theorem bj-exlimh

Step	Hyp	Ref	Expression
1		exim 1761	. 2 |- ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ps ) )
2	1	imim1d 82	1 |- ( A. x ( ph -> ps ) -> ( ( E. x ps -> ch ) -> ( E. x ph -> 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-exlimh2  32603