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Theorem nfsab 2014
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfsab.1 xφ
Assertion
Ref Expression
nfsab x z {yφ}
Distinct variable group:   x,z
Allowed substitution hints:   φ(x,y,z)

Proof of Theorem nfsab
StepHypRef Expression
1 nfsab.1 . . . 4 xφ
21nfri 1393 . . 3 (φxφ)
32hbab 2013 . 2 (z {yφ} → x z {yφ})
43nfi 1331 1 x z {yφ}
Colors of variables: wff set class
Syntax hints:  wnf 1329   wcel 1374  {cab 2008
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009
This theorem is referenced by:  nfab  2164  peano2  4245
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