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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 4590 | . . . 4 | |
2 | 1 | gen2 1443 | . . 3 |
3 | dftr2 4089 | . . 3 | |
4 | 2, 3 | mpbir 145 | . 2 |
5 | treq 4093 | . . . 4 | |
6 | treq 4093 | . . . 4 | |
7 | treq 4093 | . . . 4 | |
8 | tr0 4098 | . . . 4 | |
9 | suctr 4406 | . . . . 5 | |
10 | 9 | a1i 9 | . . . 4 |
11 | 5, 6, 7, 6, 8, 10 | finds 4584 | . . 3 |
12 | 11 | rgen 2523 | . 2 |
13 | dford3 4352 | . 2 | |
14 | 4, 12, 13 | mpbir2an 937 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1346 wcel 2141 wral 2448 c0 3414 wtr 4087 word 4347 csuc 4350 com 4574 |
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 4107 ax-nul 4115 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-iinf 4572 |
This theorem depends on definitions: df-bi 116 df-3an 975 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 3568 df-sn 3589 df-pr 3590 df-uni 3797 df-int 3832 df-tr 4088 df-iord 4351 df-suc 4356 df-iom 4575 |
This theorem is referenced by: omelon2 4592 limom 4598 freccllem 6381 frecfcllem 6383 frecsuclem 6385 fict 6846 infnfi 6873 isinfinf 6875 hashinfuni 10711 hashinfom 10712 hashennn 10714 ennnfonelemrn 12374 ctinf 12385 |
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