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Mirrors > Home > MPE Home > Th. List > ordn2lp | Unicode version |
Description: An ordinal class cannot an element of one of its members. Variant of first part of Theorem 2.2(vii) of [BellMachover] p. 469. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
ordn2lp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordirr 4563 |
. 2
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2 | ordtr 4559 |
. . 3
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3 | trel 4273 |
. . 3
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4 | 2, 3 | syl 16 |
. 2
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5 | 1, 4 | mtod 170 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: ordtri1 4578 ordnbtwn 4635 suc11 4648 smoord 6590 unblem1 7322 cantnfp1lem3 7596 cardprclem 7826 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 ax-sep 4294 ax-nul 4302 ax-pr 4367 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2262 df-mo 2263 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-ne 2573 df-ral 2675 df-rex 2676 df-rab 2679 df-v 2922 df-sbc 3126 df-dif 3287 df-un 3289 df-in 3291 df-ss 3298 df-nul 3593 df-if 3704 df-sn 3784 df-pr 3785 df-op 3787 df-uni 3980 df-br 4177 df-opab 4231 df-tr 4267 df-eprel 4458 df-fr 4505 df-we 4507 df-ord 4548 |
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