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Mirrors > Home > ILE Home > Th. List > 4on | 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 6027 | . 2 ⊢ 4𝑜 = suc 3𝑜 | |
2 | 3on 6034 | . . 3 ⊢ 3𝑜 ∈ On | |
3 | 2 | onsuci 4260 | . 2 ⊢ suc 3𝑜 ∈ On |
4 | 1, 3 | eqeltri 2151 | 1 ⊢ 4𝑜 ∈ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 Oncon0 4118 suc csuc 4120 3𝑜c3o 6019 4𝑜c4o 6020 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-nul 3904 ax-pow 3948 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-uni 3602 df-tr 3876 df-iord 4121 df-on 4123 df-suc 4126 df-1o 6024 df-2o 6025 df-3o 6026 df-4o 6027 |
This theorem is referenced by: (None) |
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