Theorem nfab 2353

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.

Step	Hyp	Ref	Expression
1		nfab.1	. . 3 |- F/ x ph
2	1	nfsab 2197	. 2 |- F/ x z e. { y | ph }
3	2	nfci 2338	1 |- F/_ x { y | ph }

Syntax hints:   F/wnf 1483   {cab 2191   F/_wnfc 2335

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-nfc 2337

This theorem is referenced by:  nfaba1  2354  nfrabw  2687  sbcel12g  3108  sbceqg  3109  nfun  3329  nfpw  3629  nfpr  3683  nfop  3835  nfuni  3856  nfint  3895  intab  3914  nfiunxy  3953  nfiinxy  3954  nfiunya  3955  nfiinya  3956  nfiu1  3957  nfii1  3958  nfopab  4112  nfopab1  4113  nfopab2  4114  repizf2  4206  nfdm  4922  fun11iun  5543  eusvobj2  5930  nfoprab1  5994  nfoprab2  5995  nfoprab3  5996  nfoprab  5997  nfrecs  6393  nffrec  6482  nfixpxy  6804  nfixp1  6805  nfwrd  11022