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Theorem cbvsetlike 25456
 Description: Change the bound variable in the statement stating that is set-like. (Contributed by Scott Fenton, 2-Feb-2011.)
Assertion
Ref Expression
cbvsetlike
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbvsetlike
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 predeq3 25443 . . . 4
21eleq1d 2502 . . 3
32cbvralv 2932 . 2
4 predeq3 25443 . . . 4
54eleq1d 2502 . . 3
65cbvralv 2932 . 2
73, 6bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wcel 1725  wral 2705  cvv 2956  cpred 25438 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-pred 25439
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