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Theorem nfsbc1d 3170
Description: Deduction version of nfsbc1 3171. (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 3154 . 2  |-  ( [. A  /  x ]. ps  <->  A  e.  { x  |  ps } )
2 nfsbc1d.2 . . 3  |-  ( ph  -> 
F/_ x A )
3 nfab1 2573 . . . 4  |-  F/_ x { x  |  ps }
43a1i 11 . . 3  |-  ( ph  -> 
F/_ x { x  |  ps } )
52, 4nfeld 2586 . 2  |-  ( ph  ->  F/ x  A  e. 
{ x  |  ps } )
61, 5nfxfrd 1580 1  |-  ( ph  ->  F/ x [. A  /  x ]. ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1553    e. wcel 1725   {cab 2421   F/_wnfc 2558   [.wsbc 3153
This theorem is referenced by:  nfsbc1  3171  nfcsb1d  3273
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-sbc 3154
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