Theorem bj-nexdvt 32688

Description: Closed form of nexdv 1864. (Contributed by BJ, 20-Oct-2019.)

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem bj-nexdvt

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ph
2		bj-nexdt 32687	. 2 |- ( F/ x ph -> ( A. x ( ph -> -. ps ) -> ( ph -> -. E. x ps ) ) )
3	1, 2	ax-mp 5	1 |- ( A. x ( ph -> -. ps ) -> ( ph -> -. E. x ps ) )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)