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Theorem nfabd 2623
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 471 . 2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
41, 3nfabd2 2622 1  |-  ( ph  -> 
F/_ x { y  |  ps } )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1453   F/wnf 1678   {cab 2448   F/_wnfc 2590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-nf 1679  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592
This theorem is referenced by:  nfsbcd  3300  nfcsb1d  3389  nfcsbd  3392  nfifd  3921  nfunid  4219  nfiotad  5568
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