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Theorem onintss 4335
 Description: If a property is true for an ordinal number, then the minimum ordinal number for which it is true is smaller or equal. Theorem Schema 61 of [Suppes] p. 228. (Contributed by NM, 3-Oct-2003.)
Hypothesis
Ref Expression
onintss.1
Assertion
Ref Expression
onintss
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem onintss
StepHypRef Expression
1 onintss.1 . . 3
21intminss 3786 . 2
32ex 425 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wceq 1619   wcel 1621  crab 2512   wss 3078  cint 3760  con0 4285 This theorem is referenced by:  rankval3b  7382  cardne  7482 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rab 2516  df-v 2729  df-in 3085  df-ss 3089  df-int 3761
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