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Mirrors > Home > ILE Home > Th. List > 1on | Unicode version |
Description: Ordinal 1 is an ordinal number. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
1on |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1o 6392 | . 2 | |
2 | 0elon 4375 | . . 3 | |
3 | 2 | onsuci 4498 | . 2 |
4 | 1, 3 | eqeltri 2243 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 c0 3414 con0 4346 csuc 4348 c1o 6385 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-nul 4113 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3566 df-sn 3587 df-pr 3588 df-uni 3795 df-tr 4086 df-iord 4349 df-on 4351 df-suc 4354 df-1o 6392 |
This theorem is referenced by: 1oex 6400 2on 6401 2on0 6402 2oconcl 6415 fnoei 6428 oeiexg 6429 oeiv 6432 oei0 6435 oeicl 6438 o1p1e2 6444 oawordriexmid 6446 enpr2d 6791 endisj 6798 snexxph 6923 djuex 7016 1stinr 7049 2ndinr 7050 pm54.43 7154 xpdjuen 7182 prarloclemarch2 7368 bj-el2oss1o 13730 nnsf 13960 |
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