ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  onunisuci Structured version   GIF version

Theorem onunisuci 4117
Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994.)
Hypothesis
Ref Expression
on.1 A On
Assertion
Ref Expression
onunisuci suc A = A

Proof of Theorem onunisuci
StepHypRef Expression
1 on.1 . . 3 A On
21ontrci 4112 . 2 Tr A
31elexi 2542 . . 3 A V
43unisuc 4097 . 2 (Tr A suc A = A)
52, 4mpbi 133 1 suc A = A
Colors of variables: wff set class
Syntax hints:   = wceq 1228   wcel 1374   cuni 3552  Tr wtr 3826  Oncon0 4047  suc csuc 4049
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2287  df-rex 2288  df-v 2535  df-un 2897  df-in 2899  df-ss 2906  df-sn 3354  df-pr 3355  df-uni 3553  df-tr 3827  df-iord 4050  df-on 4052  df-suc 4055
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator