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Theorem nfsab 2463
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 1972 . . 3  |-  ( ph  ->  A. x ph )
32hbab 2462 . 2  |-  ( z  e.  { y  | 
ph }  ->  A. x  z  e.  { y  |  ph } )
43nfi 1682 1  |-  F/ x  z  e.  { y  |  ph }
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1675    e. wcel 1904   {cab 2457
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458
This theorem is referenced by:  nfab  2616  upbdrech  37611  ssfiunibd  37615
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