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Theorem nfsab 2434
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfsab.1  |-  F/ x ph
Assertion
Ref Expression
nfsab  |-  F/ x  z  e.  { y  |  ph }
Distinct variable group:    x, z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem nfsab
StepHypRef Expression
1 nfsab.1 . . . 4  |-  F/ x ph
21nfri 1780 . . 3  |-  ( ph  ->  A. x ph )
32hbab 2433 . 2  |-  ( z  e.  { y  | 
ph }  ->  A. x  z  e.  { y  |  ph } )
43nfi 1561 1  |-  F/ x  z  e.  { y  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1554    e. wcel 1727   {cab 2428
This theorem is referenced by:  nfab  2582
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429
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