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Theorem 4on 8432
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 8416 . 2 4o = suc 3o
2 3on 8431 . . 3 3o ∈ On
32onsuci 7775 . 2 suc 3o ∈ On
41, 3eqeltri 2834 1 4o ∈ On
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Oncon0 6318  suc csuc 6320  3oc3o 8408  4oc4o 8409
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5257  ax-nul 5264  ax-pr 5385  ax-un 7673
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-ral 3066  df-rex 3075  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-pss 3930  df-nul 4284  df-if 4488  df-pw 4563  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-opab 5169  df-tr 5224  df-eprel 5538  df-po 5546  df-so 5547  df-fr 5589  df-we 5591  df-ord 6321  df-on 6322  df-suc 6324  df-1o 8413  df-2o 8414  df-3o 8415  df-4o 8416
This theorem is referenced by:  4no  41718
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