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Theorem cbvab 2598
Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.) (Proof shortened by Wolf Lammen, 16-Nov-2019.)
Hypotheses
Ref Expression
cbvab.1
cbvab.2
cbvab.3
Assertion
Ref Expression
cbvab

Proof of Theorem cbvab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvab.1 . . . . 5
21sbco2 2158 . . . 4
3 cbvab.2 . . . . . 6
4 cbvab.3 . . . . . 6
53, 4sbie 2149 . . . . 5
65sbbii 1746 . . . 4
72, 6bitr3i 251 . . 3
8 df-clab 2443 . . 3
9 df-clab 2443 . . 3
107, 8, 93bitr4i 277 . 2
1110eqriv 2453 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  [wsb 1739  e.wcel 1818  {cab 2442
This theorem is referenced by:  cbvabv  2600  cbvrab  3107  cbvsbc  3356  cbvrabcsf  3469  rabsnifsb  4098  rabasiun  4334  dfdmf  5201  dfrnf  5246  funfv2f  5942  abrexex2g  6777  abrexex2  6781  ptrest  30048  bnj873  33982
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449
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