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Theorem nfab 2198
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfab.1 𝑥𝜑
Assertion
Ref Expression
nfab 𝑥{𝑦𝜑}

Proof of Theorem nfab
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 nfab.1 . . 3 𝑥𝜑
21nfsab 2048 . 2 𝑥 𝑧 ∈ {𝑦𝜑}
32nfci 2184 1 𝑥{𝑦𝜑}
Colors of variables: wff set class
Syntax hints:  wnf 1365  {cab 2042  wnfc 2181
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-nfc 2183
This theorem is referenced by:  nfaba1  2199  nfrabxy  2507  sbcel12g  2893  sbceqg  2894  nfun  3127  nfpw  3399  nfpr  3448  nfop  3593  nfuni  3614  nfint  3653  intab  3672  nfiunxy  3711  nfiinxy  3712  nfiunya  3713  nfiinya  3714  nfiu1  3715  nfii1  3716  nfopab  3853  nfopab1  3854  nfopab2  3855  repizf2  3943  nfdm  4606  fun11iun  5175  eusvobj2  5526  nfoprab1  5582  nfoprab2  5583  nfoprab3  5584  nfoprab  5585  nfrecs  5953  nffrec  6013
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