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Theorem cbvab 2553
 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 2184 . . . 4
3 cbvab.1 . . . . . 6
4 cbvab.3 . . . . . . . 8
54equcoms 1693 . . . . . . 7
65bicomd 193 . . . . . 6
73, 6sbie 2122 . . . . 5
8 sbequ 2138 . . . . 5
97, 8syl5bbr 251 . . . 4
102, 9sbie 2122 . . 3
11 df-clab 2422 . . 3
12 df-clab 2422 . . 3
1310, 11, 123bitr4i 269 . 2
1413eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wnf 1553   wceq 1652  wsb 1658   wcel 1725  cab 2421 This theorem is referenced by:  cbvabv  2554  cbvrab  2946  cbvsbc  3181  cbvrabcsf  3306  dfdmf  5056  dfrnf  5100  funfv2f  5784  abrexex2g  5980  abrexex2  5993  bnj873  29232 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428
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