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Mirrors > Home > MPE Home > Th. List > oneli | Structured version Visualization version Unicode version |
Description: A member of an ordinal number is an ordinal number. Theorem 7M(a) of [Enderton] p. 192. (Contributed by NM, 11-Jun-1994.) |
Ref | Expression |
---|---|
on.1 |
Ref | Expression |
---|---|
oneli |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 | . 2 | |
2 | onelon 5748 | . 2 | |
3 | 1, 2 | mpan 706 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 con0 5723 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-tr 4753 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-ord 5726 df-on 5727 |
This theorem is referenced by: onssneli 5837 oawordeulem 7634 rankuni 8726 tcrank 8747 cardne 8791 cardval2 8817 alephsuc2 8903 cfsmolem 9092 cfcof 9096 alephreg 9404 pwcfsdom 9405 tskcard 9603 onsucconni 32436 |
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