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Theorem nfsab1 2046
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 2045 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1367 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1365    e. wcel 1409   {cab 2042
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-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
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043
This theorem is referenced by:  abbi  2167  nfab1  2196  ralab2  2727  rexab2  2729  rabn0m  3272  eluniab  3619  elintab  3653  intexabim  3933  iinexgm  3935  opabex3d  5775  opabex3  5776
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