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Theorem onintss 4634
 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 4078 . 2
32ex 425 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   wcel 1726  crab 2711   wss 3322  cint 4052  con0 4584 This theorem is referenced by:  rankval3b  7755  cardne  7857 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-in 3329  df-ss 3336  df-int 4053
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