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Theorem nfsab1 2426
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 2425 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1560 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1553    e. wcel 1725   {cab 2422
This theorem is referenced by:  abbi  2546  nfab1  2574  ralab2  3099  rexab2  3101  eluniab  4027  elintab  4061  opabex3d  5989  opabex3  5990  setindtrs  27096
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423
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