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Mirrors > Home > ILE Home > Th. List > ordom | Unicode version |
Description: Omega is ordinal. Theorem 7.32 of [TakeutiZaring] p. 43. (Contributed by NM, 18-Oct-1995.) |
Ref | Expression |
---|---|
ordom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnn 4567 | . . . 4 | |
2 | 1 | gen2 1430 | . . 3 |
3 | dftr2 4066 | . . 3 | |
4 | 2, 3 | mpbir 145 | . 2 |
5 | treq 4070 | . . . 4 | |
6 | treq 4070 | . . . 4 | |
7 | treq 4070 | . . . 4 | |
8 | tr0 4075 | . . . 4 | |
9 | suctr 4383 | . . . . 5 | |
10 | 9 | a1i 9 | . . . 4 |
11 | 5, 6, 7, 6, 8, 10 | finds 4561 | . . 3 |
12 | 11 | rgen 2510 | . 2 |
13 | dford3 4329 | . 2 | |
14 | 4, 12, 13 | mpbir2an 927 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1333 wcel 2128 wral 2435 c0 3395 wtr 4064 word 4324 csuc 4327 com 4551 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-nul 4092 ax-pow 4137 ax-pr 4171 ax-un 4395 ax-iinf 4549 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3396 df-pw 3546 df-sn 3567 df-pr 3568 df-uni 3775 df-int 3810 df-tr 4065 df-iord 4328 df-suc 4333 df-iom 4552 |
This theorem is referenced by: omelon2 4569 limom 4575 freccllem 6351 frecfcllem 6353 frecsuclem 6355 fict 6815 infnfi 6842 isinfinf 6844 hashinfuni 10662 hashinfom 10663 hashennn 10665 ennnfonelemrn 12218 ctinf 12229 |
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