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Theorem nfab 2261
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfab.1  |-  F/ x ph
Assertion
Ref Expression
nfab  |-  F/_ x { y  |  ph }

Proof of Theorem nfab
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 nfab.1 . . 3  |-  F/ x ph
21nfsab 2107 . 2  |-  F/ x  z  e.  { y  |  ph }
32nfci 2246 1  |-  F/_ x { y  |  ph }
Colors of variables: wff set class
Syntax hints:   F/wnf 1419   {cab 2101   F/_wnfc 2243
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-nfc 2245
This theorem is referenced by:  nfaba1  2262  nfrabxy  2586  sbcel12g  2986  sbceqg  2987  nfun  3200  nfpw  3491  nfpr  3541  nfop  3689  nfuni  3710  nfint  3749  intab  3768  nfiunxy  3807  nfiinxy  3808  nfiunya  3809  nfiinya  3810  nfiu1  3811  nfii1  3812  nfopab  3964  nfopab1  3965  nfopab2  3966  repizf2  4054  nfdm  4751  fun11iun  5354  eusvobj2  5726  nfoprab1  5786  nfoprab2  5787  nfoprab3  5788  nfoprab  5789  nfrecs  6170  nffrec  6259  nfixpxy  6577  nfixp1  6578
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