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Theorem nfsab 2358
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 1768 . . 3  |-  ( ph  ->  A. x ph )
32hbab 2357 . 2  |-  ( z  e.  { y  | 
ph }  ->  A. x  z  e.  { y  |  ph } )
43nfi 1556 1  |-  F/ x  z  e.  { y  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1549    e. wcel 1715   {cab 2352
This theorem is referenced by:  nfab  2506
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353
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