| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > df-2o | Structured version Visualization version GIF version | ||
| Description: Define the ordinal number 2. Lemma 3.17 of [Schloeder] p. 10. (Contributed by NM, 18-Feb-2004.) |
| Ref | Expression |
|---|---|
| df-2o | ⊢ 2o = suc 1o |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | c2o 8470 | . 2 class 2o | |
| 2 | c1o 8469 | . . 3 class 1o | |
| 3 | 2 | csuc 6364 | . 2 class suc 1o |
| 4 | 1, 3 | wceq 1569 | 1 wff 2o = suc 1o |
| Colors of variables: wff setvar class |
| This definition is used by: df2o3 8484 2on 8490 2on0 8491 ondif2 8510 o1p1e2 8548 o2p2e4 8549 oneo 8589 om2 8594 2onnALT 8652 1one2o 8655 nnm2 8662 nnneo 8664 nneob 8665 1sdom2ALT 9240 en2 9271 pm54.43 10082 en2eleq 10087 en2other2 10088 infxpenc 10097 infxpenc2 10101 dju1p1e2ALT 10253 fin1a2lem4 10481 cfpwsdom 10669 canthp1lem2 10738 pwxpndom2 10750 tsk2 10850 hash2 14549 f1otrspeq 19661 pmtrf 19669 pmtrmvd 19670 pmtrfinv 19675 efgmnvl 19928 isnzr2 20768 ltsval2 28013 nosgnn0 28015 ltssolem1 28032 nosepnelem 28036 nolt02o 28052 nogt01o 28053 bdaypw2n0bndlem 28849 unidifsnel 33131 unidifsnne 33132 r12 35726 ex-sategoelel12 36192 1oequni2o 38292 finxpreclem3 38317 finxpreclem4 38318 finxpsuclem 38321 finxp2o 38323 pw2f1ocnv 44044 pwfi2f1o 44098 oege2 44309 oaomoencom 44319 oaltom 44406 oe2 44407 omltoe 44408 nlim2NEW 44444 clsk1indlem1 45045 |
| Copyright terms: Public domain | W3C validator |