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Theorem nfsab1 2072
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 2071 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1392 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1390    e. wcel 1434   {cab 2068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069
This theorem is referenced by:  abbi  2193  nfab1  2222  ralab2  2757  rexab2  2759  rabn0m  3273  eluniab  3615  elintab  3649  intexabim  3929  iinexgm  3931  opabex3d  5773  opabex3  5774
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