Metamath Proof Explorer

Theorem bj-nnf-exlim

Description: Proof of the closed form of exlimi from modalK (compare exlimiv ). See also bj-sylget2 . (Contributed by BJ, 2-Dec-2023)

Ref Expression
Assertion bj-nnf-exlim 
|- ( F// x ps -> ( A. x ( ph -> ps ) -> ( E. x ph -> ps ) ) )

Proof

Step Hyp Ref Expression
1 exim 
 |-  ( A. x ( ph -> ps ) -> ( E. x ph -> E. x ps ) )
2 bj-nnfe 
 |-  ( F// x ps -> ( E. x ps -> ps ) )
3 1 2 syl9r 
 |-  ( F// x ps -> ( A. x ( ph -> ps ) -> ( E. x ph -> ps ) ) )