Theorem nfab 2380

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 2223	. 2 |- F/ x z e. { y | ph }
3	2	nfci 2365	1 |- F/_ x { y | ph }

Syntax hints:   F/wnf 1509   {cab 2217   F/_wnfc 2362

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-nfc 2364

This theorem is referenced by:  nfaba1  2381  nfrabw  2715  sbcel12g  3143  sbceqg  3144  nfun  3365  nfpw  3669  nfpr  3723  nfop  3883  nfuni  3904  nfint  3943  intab  3962  nfiunxy  4001  nfiinxy  4002  nfiunya  4003  nfiinya  4004  nfiu1  4005  nfii1  4006  nfopab  4162  nfopab1  4163  nfopab2  4164  repizf2  4258  nfdm  4982  fun11iun  5613  eusvobj2  6014  nfoprab1  6080  nfoprab2  6081  nfoprab3  6082  nfoprab  6083  nfrecs  6516  nffrec  6605  nfixpxy  6929  nfixp1  6930  nfwrd  11208