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Theorem nfabd 2438
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 8-Oct-2016.)
Hypotheses
Ref Expression
nfabd.1  |-  F/ y
ph
nfabd.2  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfabd  |-  ( ph  -> 
F/_ x { y  |  ps } )

Proof of Theorem nfabd
StepHypRef Expression
1 nfabd.1 . 2  |-  F/ y
ph
2 nfabd.2 . . 3  |-  ( ph  ->  F/ x ps )
32adantr 451 . 2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
41, 3nfabd2 2437 1  |-  ( ph  -> 
F/_ x { y  |  ps } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   F/wnf 1531    = wceq 1623   {cab 2269   F/_wnfc 2406
This theorem is referenced by:  nfsbcd  3011  nfcsb1d  3111  nfcsbd  3114  nfifd  3588  nfunid  3834  nfiotad  5222
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408
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