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Theorem nfabd 2613
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 466 . 2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
41, 3nfabd2 2612 1  |-  ( ph  -> 
F/_ x { y  |  ps } )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1435   F/wnf 1663   {cab 2414   F/_wnfc 2577
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579
This theorem is referenced by:  nfsbcd  3326  nfcsb1d  3415  nfcsbd  3418  nfifd  3943  nfunid  4229  nfiotad  5568
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