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Mirrors > Home > MPE Home > Th. List > ordsucsssuc | Structured version Unicode version |
Description: The subclass relationship between two ordinal classes is inherited by their successors. (Contributed by NM, 4-Oct-2003.) |
Ref | Expression |
---|---|
ordsucsssuc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordsucelsuc 6536 |
. . . 4
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2 | 1 | notbid 294 |
. . 3
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3 | 2 | adantr 465 |
. 2
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4 | ordtri1 4853 |
. 2
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5 | ordsuc 6528 |
. . 3
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6 | ordsuc 6528 |
. . 3
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7 | ordtri1 4853 |
. . 3
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8 | 5, 6, 7 | syl2anb 479 |
. 2
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9 | 3, 4, 8 | 3bitr4d 285 |
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-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4514 ax-nul 4522 ax-pr 4632 ax-un 6475 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3073 df-sbc 3288 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-pss 3445 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-tp 3983 df-op 3985 df-uni 4193 df-br 4394 df-opab 4452 df-tr 4487 df-eprel 4733 df-po 4742 df-so 4743 df-fr 4780 df-we 4782 df-ord 4823 df-on 4824 df-suc 4826 |
This theorem is referenced by: oawordri 7092 oeworde 7135 nnawordi 7163 bndrank 8152 rankmapu 8189 ackbij1b 8512 onsuct0 28424 |
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