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Theorem nfsab1 2107
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfsab1  |-  F/ x  y  e.  { x  |  ph }
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem nfsab1
StepHypRef Expression
1 hbab1 2106 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1423 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1421    e. wcel 1465   {cab 2103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104
This theorem is referenced by:  abbi  2231  nfab1  2260  ralab2  2821  rexab2  2823  abn0m  3358  rabn0m  3360  eluniab  3718  elintab  3752  intexabim  4047  iinexgm  4049  opabex3d  5987  opabex3  5988
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