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Theorem frminexOLD 26429
 Description: If an element of a founded set satisfies a property , then there is a minimal element that satisfies . (Moved to frminex 4373 in main set.mm and may be deleted by mathbox owner, JM. --NM 16-Mar-2013.) (Contributed by Jeff Madsen, 18-Jun-2010.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
frminexOLD.1
frminexOLD.2
Assertion
Ref Expression
frminexOLD
Distinct variable groups:   ,,   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem frminexOLD
StepHypRef Expression
1 frminexOLD.1 . 2
2 frminexOLD.2 . 2
31, 2frminex 4373 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358   wcel 1684  wral 2543  wrex 2544  cvv 2788   class class class wbr 4023   wfr 4349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-fr 4352
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