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Theorem nfsab1 2027
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 2026 . 2 (y {xφ} → x y {xφ})
21nfi 1348 1 x y {xφ}
Colors of variables: wff set class
Syntax hints:  wnf 1346   wcel 1390  {cab 2023
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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024
This theorem is referenced by:  abbi  2148  nfab1  2177  ralab2  2699  rexab2  2701  rabn0m  3239  eluniab  3583  elintab  3617  intexabim  3897  iinexgm  3899  opabex3d  5690  opabex3  5691
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