Theorem nfab 2179

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfab.1	⊢ Ⅎxφ

Assertion

Ref	Expression
nfab	⊢ Ⅎx{y ∣ φ}

Proof of Theorem nfab

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfab.1	. . 3 ⊢ Ⅎxφ
2	1	nfsab 2029	. 2 ⊢ Ⅎx z ∈ {y ∣ φ}
3	2	nfci 2165	1 ⊢ Ⅎx{y ∣ φ}

Syntax hints:  Ⅎwnf 1346  {cab 2023  Ⅎwnfc 2162

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-nfc 2164

This theorem is referenced by:  nfaba1  2180  nfrabxy  2484  sbcel12g  2859  sbceqg  2860  nfun  3093  nfpw  3363  nfpr  3411  nfop  3556  nfuni  3577  nfint  3616  intab  3635  nfiunxy  3674  nfiinxy  3675  nfiunya  3676  nfiinya  3677  nfiu1  3678  nfii1  3679  nfopab  3816  nfopab1  3817  nfopab2  3818  repizf2  3906  nfdm  4521  fun11iun  5090  eusvobj2  5441  nfoprab1  5496  nfoprab2  5497  nfoprab3  5498  nfoprab  5499  nfrecs  5863  nffrec  5921