Theorem bj-nexdh 32606

Description: Closed form of nexdh 1792 (actually, its general instance). (Contributed by BJ, 6-May-2019.)

Assertion

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

Proof of Theorem bj-nexdh

Step	Hyp	Ref	Expression
1		sylgt 1749	. 2 |- ( A. x ( ph -> -. ps ) -> ( ( ch -> A. x ph ) -> ( ch -> A. x -. ps ) ) )
2		alnex 1706	. 2 |- ( A. x -. ps <-> -. E. x ps )
3	1, 2	syl8ib 246	1 |- ( A. x ( ph -> -. ps ) -> ( ( ch -> A. x ph ) -> ( ch -> -. E. x ps ) ) )

Syntax hints:   -. wn 3   -> 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-4 1737

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

This theorem is referenced by:  bj-nexdh2  32607  bj-nexdt  32687