Theorem bj-nfdt 32686

Description: Closed form of nf5d 2118 and nf5dh 2026. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-nfdt	|- ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( ( ph -> A. x ph ) -> ( ph -> F/ x ps ) ) )

Proof of Theorem bj-nfdt

Step	Hyp	Ref	Expression
1		bj-nfdt0 32685	. 2 |- ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( A. x ph -> F/ x ps ) )
2	1	imim2d 57	1 |- ( A. x ( ph -> ( ps -> A. x ps ) ) -> ( ( ph -> A. x ph ) -> ( ph -> F/ x ps ) ) )

Syntax hints:   -> wi 4   A.wal 1481   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-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)