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Theorem cbvab 2157
Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.)
Hypotheses
Ref Expression
cbvab.1  F/
cbvab.2  F/
cbvab.3
Assertion
Ref Expression
cbvab  {  |  }  {  |  }

Proof of Theorem cbvab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvab.2 . . . . 5  F/
21nfsb 1819 . . . 4  F/
3 cbvab.1 . . . . . 6  F/
4 cbvab.3 . . . . . . . 8
54equcoms 1591 . . . . . . 7
65bicomd 129 . . . . . 6
73, 6sbie 1671 . . . . 5
8 sbequ 1718 . . . . 5
97, 8syl5bbr 183 . . . 4
102, 9sbie 1671 . . 3
11 df-clab 2024 . . 3  {  |  }
12 df-clab 2024 . . 3  {  |  }
1310, 11, 123bitr4i 201 . 2  {  |  }  {  |  }
1413eqriv 2034 1  {  |  }  {  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242   F/wnf 1346   wcel 1390  wsb 1642   {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  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030
This theorem is referenced by:  cbvabv  2158  cbvrab  2549  cbvsbc  2785  cbvrabcsf  2905  dfdmf  4471  dfrnf  4518  funfvdm2f  5181  abrexex2g  5689  abrexex2  5693
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