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Theorem nfsab1 2012
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfsab1 x y {xφ}
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem nfsab1
StepHypRef Expression
1 hbab1 2011 . 2 (y {xφ} → x y {xφ})
21nfi 1331 1 x y {xφ}
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-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009
This theorem is referenced by:  abbi  2133  nfab1  2162  ralab2  2682  rexab2  2684  rabn0m  3222  eluniab  3566  elintab  3600  intexabim  3880  iinexgm  3882  opabex3d  5671  opabex3  5672
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