Theorem nfnd 1785

Description: Deduction associated with nfnt 1782. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
nfnd.1	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfnd	|- ( ph -> F/ x -. ps )

Proof of Theorem nfnd

Step	Hyp	Ref	Expression
1		nfnd.1	. 2 |- ( ph -> F/ x ps )
2		nfnt 1782	. 2 |- ( F/ x ps -> F/ x -. ps )
3	1, 2	syl 17	1 |- ( ph -> F/ x -. ps )

Syntax hints:   -. wn 3   -> wi 4   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

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

This theorem is referenced by:  nfand  1826  hbnt  2144  nfexd  2167  cbvexd  2278  nfexd2  2332  nfned  2895  nfneld  2905  nfrexd  3006  axpowndlem3  9421  axpowndlem4  9422  axregndlem2  9425  axregnd  9426  distel  31709  bj-cbvexdv  32736