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Theorem nfsab1 2393
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 2392 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1646 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1639    e. wcel 1844   {cab 2389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-12 1880  ax-13 2028
This theorem depends on definitions:  df-bi 187  df-an 371  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390
This theorem is referenced by:  abbiOLD  2536  clelab  2548  nfab1  2568  ralab2  3216  rexab2  3218  eluniab  4204  elintab  4240  opabex3d  6764  opabex3  6765  setindtrs  35342
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