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Theorem cbvab 2263
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by Andrew Salmon, 11-Jul-2011.)
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.2 . . . . 5
21nfsb 1919 . . . 4
3 cbvab.1 . . . . . 6
4 cbvab.3 . . . . . . . 8
54equcoms 1684 . . . . . . 7
65bicomd 140 . . . . . 6
73, 6sbie 1764 . . . . 5
8 sbequ 1812 . . . . 5
97, 8bitr3id 193 . . . 4
102, 9sbie 1764 . . 3
11 df-clab 2126 . . 3
12 df-clab 2126 . . 3
1310, 11, 123bitr4i 211 . 2
1413eqriv 2136 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331  wnf 1436   wcel 1480  wsb 1735  cab 2125 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132 This theorem is referenced by:  cbvabv  2264  cbvrab  2684  cbvsbc  2937  cbvrabcsf  3065  dfdmf  4732  dfrnf  4780  funfvdm2f  5486  abrexex2g  6018  abrexex2  6022
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