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Theorem nfsbc1d 3121
Description: Deduction version of nfsbc1 3122. (Contributed by NM, 23-May-2006.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1d.2  |-  ( ph  -> 
F/_ x A )
Assertion
Ref Expression
nfsbc1d  |-  ( ph  ->  F/ x [. A  /  x ]. ps )

Proof of Theorem nfsbc1d
StepHypRef Expression
1 df-sbc 3105 . 2  |-  ( [. A  /  x ]. ps  <->  A  e.  { x  |  ps } )
2 nfsbc1d.2 . . 3  |-  ( ph  -> 
F/_ x A )
3 nfab1 2525 . . . 4  |-  F/_ x { x  |  ps }
43a1i 11 . . 3  |-  ( ph  -> 
F/_ x { x  |  ps } )
52, 4nfeld 2538 . 2  |-  ( ph  ->  F/ x  A  e. 
{ x  |  ps } )
61, 5nfxfrd 1577 1  |-  ( ph  ->  F/ x [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1550    e. wcel 1717   {cab 2373   F/_wnfc 2510   [.wsbc 3104
This theorem is referenced by:  nfsbc1  3122  nfcsb1d  3224
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-sbc 3105
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