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Mirrors > Home > MPE Home > Th. List > 4on | Structured version Visualization version GIF version |
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.) |
Ref | Expression |
---|---|
4on | ⊢ 4o ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4o 8202 | . 2 ⊢ 4o = suc 3o | |
2 | 3on 8209 | . . 3 ⊢ 3o ∈ On | |
3 | 2 | onsuci 7614 | . 2 ⊢ suc 3o ∈ On |
4 | 1, 3 | eqeltri 2834 | 1 ⊢ 4o ∈ On |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2110 Oncon0 6210 suc csuc 6212 3oc3o 8194 4oc4o 8195 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-11 2158 ax-ext 2708 ax-sep 5189 ax-nul 5196 ax-pr 5319 ax-un 7520 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3or 1090 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-ne 2940 df-ral 3063 df-rex 3064 df-rab 3067 df-v 3407 df-dif 3866 df-un 3868 df-in 3870 df-ss 3880 df-pss 3882 df-nul 4235 df-if 4437 df-pw 4512 df-sn 4539 df-pr 4541 df-tp 4543 df-op 4545 df-uni 4817 df-br 5051 df-opab 5113 df-tr 5159 df-eprel 5457 df-po 5465 df-so 5466 df-fr 5506 df-we 5508 df-ord 6213 df-on 6214 df-suc 6216 df-1o 8199 df-2o 8200 df-3o 8201 df-4o 8202 |
This theorem is referenced by: (None) |
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