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Theorem setlikess 25470
 Description: If is set-like over , then it is set-like over any subclass of . (Contributed by Scott Fenton, 28-Mar-2011.)
Assertion
Ref Expression
setlikess
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem setlikess
StepHypRef Expression
1 ssralv 3407 . . 3
2 predpredss 25445 . . . . 5
3 ssexg 4349 . . . . . 6
43ex 424 . . . . 5
52, 4syl 16 . . . 4
65ralimdv 2785 . . 3
71, 6syld 42 . 2
87imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725  wral 2705  cvv 2956   wss 3320  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  ax-sep 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  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-v 2958  df-in 3327  df-ss 3334  df-pred 25439
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