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Theorem nfdh 1747
Description: Deduce that  x is not free in  ph in a context. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nfdh.1  |-  ( ph  ->  A. x ph )
nfdh.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
nfdh  |-  ( ph  ->  F/ x ps )

Proof of Theorem nfdh
StepHypRef Expression
1 nfdh.1 . . 3  |-  ( ph  ->  A. x ph )
21nfi 1538 . 2  |-  F/ x ph
3 nfdh.2 . 2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
42, 3nfd 1746 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   F/wnf 1531
This theorem is referenced by:  ax11indalem  2136  ax11inda2ALT  2137  a12lem1  29130
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-nf 1532
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