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Theorem nfsbc1d 2803
Description: Deduction version of nfsbc1 2804. (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 2788 . 2  |-  ( [. A  /  x ]. ps  <->  A  e.  { x  |  ps } )
2 nfsbc1d.2 . . 3  |-  ( ph  -> 
F/_ x A )
3 nfab1 2196 . . . 4  |-  F/_ x { x  |  ps }
43a1i 9 . . 3  |-  ( ph  -> 
F/_ x { x  |  ps } )
52, 4nfeld 2209 . 2  |-  ( ph  ->  F/ x  A  e. 
{ x  |  ps } )
61, 5nfxfrd 1380 1  |-  ( ph  ->  F/ x [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1365    e. wcel 1409   {cab 2042   F/_wnfc 2181   [.wsbc 2787
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-sbc 2788
This theorem is referenced by:  nfsbc1  2804  nfcsb1d  2908
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