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Theorem setlikess 25409
 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 3367 . . 3
2 predpredss 25386 . . . . 5
3 ssexg 4309 . . . . . 6
43ex 424 . . . . 5
52, 4syl 16 . . . 4
65ralimdv 2745 . . 3
71, 6syld 42 . 2
87imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1721  wral 2666  cvv 2916   wss 3280  cpred 25381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-v 2918  df-in 3287  df-ss 3294  df-pred 25382
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