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Theorem nfabd 2651
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 465 . 2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
41, 3nfabd2 2650 1  |-  ( ph  -> 
F/_ x { y  |  ps } )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377   F/wnf 1599   {cab 2452   F/_wnfc 2615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617
This theorem is referenced by:  nfsbcd  3357  nfcsb1d  3454  nfcsbd  3457  nfifd  3973  nfunid  4258  nfiotad  5560
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