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Theorem oi0 7497
 Description: Definition of the ordinal isomorphism when its arguments are not meaningful. (Contributed by Mario Carneiro, 25-Jun-2015.)
Hypothesis
Ref Expression
oicl.1 OrdIso
Assertion
Ref Expression
oi0 Se

Proof of Theorem oi0
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oicl.1 . . 3 OrdIso
2 df-oi 7479 . . 3 OrdIso Se recs recs
31, 2eqtri 2456 . 2 Se recs recs
4 iffalse 3746 . 2 Se Se recs recs
53, 4syl5eq 2480 1 Se
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wceq 1652  wral 2705  wrex 2706  crab 2709  cvv 2956  c0 3628  cif 3739   class class class wbr 4212   cmpt 4266   Se wse 4539   wwe 4540  con0 4581   crn 4879   cres 4880  cima 4881  crio 6542  recscrecs 6632  OrdIsocoi 7478 This theorem is referenced by:  oicl  7498  oif  7499  oiexg  7504 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 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-if 3740  df-oi 7479
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