Theorem nfab 2352

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 2196	. 2 |- F/ x z e. { y | ph }
3	2	nfci 2337	1 |- F/_ x { y | ph }

Syntax hints:   F/wnf 1482   {cab 2190   F/_wnfc 2334

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-nfc 2336

This theorem is referenced by:  nfaba1  2353  nfrabw  2686  sbcel12g  3107  sbceqg  3108  nfun  3328  nfpw  3628  nfpr  3682  nfop  3834  nfuni  3855  nfint  3894  intab  3913  nfiunxy  3952  nfiinxy  3953  nfiunya  3954  nfiinya  3955  nfiu1  3956  nfii1  3957  nfopab  4111  nfopab1  4112  nfopab2  4113  repizf2  4205  nfdm  4921  fun11iun  5542  eusvobj2  5929  nfoprab1  5993  nfoprab2  5994  nfoprab3  5995  nfoprab  5996  nfrecs  6392  nffrec  6481  nfixpxy  6803  nfixp1  6804  nfwrd  11020