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Mirrors > Home > MPE Home > Th. List > oneli | Structured 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 |
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Ref | Expression |
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oneli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 |
. 2
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2 | onelon 4855 |
. 2
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3 | 1, 2 | mpan 670 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4524 ax-nul 4532 ax-pr 4642 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-rab 2808 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-opab 4462 df-tr 4497 df-eprel 4743 df-po 4752 df-so 4753 df-fr 4790 df-we 4792 df-ord 4833 df-on 4834 |
This theorem is referenced by: onssneli 4939 oawordeulem 7106 rankuni 8184 tcrank 8205 cardne 8249 cardval2 8275 alephsuc2 8364 cfsmolem 8553 cfcof 8557 alephreg 8860 pwcfsdom 8861 tskcard 9062 onsucconi 28447 |
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