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Theorem nfsab 2029
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 1409 . . 3 (φxφ)
32hbab 2028 . 2 (z {yφ} → x z {yφ})
43nfi 1348 1 x z {yφ}
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-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
This theorem is referenced by:  nfab  2179  peano2  4261
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