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Theorem nfsab1 2030
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 2029 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1351 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1349    e. wcel 1393   {cab 2026
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027
This theorem is referenced by:  abbi  2151  nfab1  2180  ralab2  2705  rexab2  2707  rabn0m  3245  eluniab  3592  elintab  3626  intexabim  3906  iinexgm  3908  opabex3d  5748  opabex3  5749
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