MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  4on Structured version   Visualization version   GIF version

Theorem 4on 7729
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.)
Assertion
Ref Expression
4on 4𝑜 ∈ On

Proof of Theorem 4on
StepHypRef Expression
1 df-4o 7720 . 2 4𝑜 = suc 3𝑜
2 3on 7728 . . 3 3𝑜 ∈ On
32onsuci 7189 . 2 suc 3𝑜 ∈ On
41, 3eqeltri 2846 1 4𝑜 ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2145  Oncon0 5865  suc csuc 5867  3𝑜c3o 7712  4𝑜c4o 7713
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-8 2147  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4916  ax-nul 4924  ax-pr 5035  ax-un 7100
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3or 1072  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-eu 2622  df-mo 2623  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ne 2944  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3353  df-sbc 3588  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-pss 3739  df-nul 4064  df-if 4227  df-pw 4300  df-sn 4318  df-pr 4320  df-tp 4322  df-op 4324  df-uni 4576  df-br 4788  df-opab 4848  df-tr 4888  df-eprel 5163  df-po 5171  df-so 5172  df-fr 5209  df-we 5211  df-ord 5868  df-on 5869  df-suc 5871  df-1o 7717  df-2o 7718  df-3o 7719  df-4o 7720
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator