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Mirrors > Home > MPE Home > Th. List > onordi | Structured version Visualization version Unicode version |
Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994.) |
Ref | Expression |
---|---|
on.1 |
Ref | Expression |
---|---|
onordi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 | . 2 | |
2 | eloni 5733 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 word 5722 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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-uni 4437 df-tr 4753 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-ord 5726 df-on 5727 |
This theorem is referenced by: ontrci 5833 onirri 5834 onun2i 5843 onuniorsuci 7039 onsucssi 7041 oawordeulem 7634 omopthi 7737 bndrank 8704 rankprb 8714 rankuniss 8729 rankelun 8735 rankelpr 8736 rankelop 8737 rankmapu 8741 rankxplim3 8744 rankxpsuc 8745 cardlim 8798 carduni 8807 dfac8b 8854 alephdom2 8910 alephfp 8931 dfac12lem2 8966 pm110.643ALT 9000 cfsmolem 9092 ttukeylem6 9336 ttukeylem7 9337 unsnen 9375 mreexexdOLD 16309 efgmnvl 18127 slerec 31923 hfuni 32291 finxpsuclem 33234 pwfi2f1o 37666 |
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