This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem bj-19.23t

Description: Statement 19.23t proved from modalK (obsoleting 19.23v ). (Contributed by BJ, 2-Dec-2023)

Ref Expression
Assertion bj-19.23t 
|- ( F// x ps -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )

Proof

Step Hyp Ref Expression
1 bj-nnf-exlim 
 |-  ( F// x ps -> ( A. x ( ph -> ps ) -> ( E. x ph -> ps ) ) )
2 bj-nnfa 
 |-  ( F// x ps -> ( ps -> A. x ps ) )
3 2 imim2d 
 |-  ( F// x ps -> ( ( E. x ph -> ps ) -> ( E. x ph -> A. x ps ) ) )
4 19.38 
 |-  ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) )
5 3 4 syl6 
 |-  ( F// x ps -> ( ( E. x ph -> ps ) -> A. x ( ph -> ps ) ) )
6 1 5 impbid 
 |-  ( F// x ps -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )