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Theorem cbvsetlike 28838
 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 28825 . . . 4
21eleq1d 2536 . . 3
32cbvralv 3088 . 2
4 predeq3 28825 . . . 4
54eleq1d 2536 . . 3
65cbvralv 3088 . 2
73, 6bitr4i 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wcel 1767  wral 2814  cvv 3113  cpred 28820 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448  df-opab 4506  df-xp 5005  df-cnv 5007  df-dm 5009  df-rn 5010  df-res 5011  df-ima 5012  df-pred 28821 This theorem is referenced by: (None)
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