| 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 8472 | . 2 class 2o | |
| 2 | c1o 8471 | . . 3 class 1o | |
| 3 | 2 | csuc 6354 | . 2 class suc 1o |
| 4 | 1, 3 | wceq 1540 | 1 wff 2o = suc 1o |
| Colors of variables: wff setvar class |
| This definition is referenced by: df2o3 8486 2on 8492 2onOLD 8493 2on0 8494 ondif2 8512 o1p1e2 8550 o2p2e4 8551 oneo 8591 2onnALT 8653 1one2o 8656 nnm2 8663 nnneo 8665 nneob 8666 enpr2dOLD 9062 snnen2oOLD 9234 1sdom2ALT 9247 1sdomOLD 9255 en2 9285 pm54.43 10013 en2eleq 10020 en2other2 10021 infxpenc 10030 infxpenc2 10034 dju1p1e2ALT 10187 fin1a2lem4 10415 cfpwsdom 10596 canthp1lem2 10665 pwxpndom2 10677 tsk2 10777 hash2 14421 f1otrspeq 19426 pmtrf 19434 pmtrmvd 19435 pmtrfinv 19440 efgmnvl 19693 isnzr2 20476 sltval2 27618 nosgnn0 27620 sltsolem1 27637 nosepnelem 27641 nolt02o 27657 nogt01o 27658 unidifsnel 32462 unidifsnne 32463 ex-sategoelel12 35395 1oequni2o 37332 finxpreclem3 37357 finxpreclem4 37358 finxpsuclem 37361 finxp2o 37363 pw2f1ocnv 43008 pwfi2f1o 43067 oege2 43278 oaomoencom 43288 om2 43375 oaltom 43376 oe2 43377 omltoe 43378 nlim2NEW 43414 clsk1indlem1 44016 |
| Copyright terms: Public domain | W3C validator |