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Mirrors > Home > ILE Home > Th. List > 3on | GIF version |
Description: Ordinal 3 is an ordinal number. (Contributed by Mario Carneiro, 5-Jan-2016.) |
Ref | Expression |
---|---|
3on | ⊢ 3o ∈ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3o 6443 | . 2 ⊢ 3o = suc 2o | |
2 | 2on 6450 | . . 3 ⊢ 2o ∈ On | |
3 | 2 | onsuci 4533 | . 2 ⊢ suc 2o ∈ On |
4 | 1, 3 | eqeltri 2262 | 1 ⊢ 3o ∈ On |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Oncon0 4381 suc csuc 4383 2oc2o 6435 3oc3o 6436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-uni 3825 df-tr 4117 df-iord 4384 df-on 4386 df-suc 4389 df-1o 6441 df-2o 6442 df-3o 6443 |
This theorem is referenced by: 4on 6453 onntri35 7266 onntri45 7270 |
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