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Mirrors > Home > MPE Home > Th. List > ordssun | Structured version Visualization version Unicode version |
Description: Property of a subclass of the maximum (i.e. union) of two ordinals. (Contributed by NM, 28-Nov-2003.) |
Ref | Expression |
---|---|
ordssun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordtri2or2 5519 |
. . 3
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2 | ssequn1 3604 |
. . . . . 6
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3 | sseq2 3454 |
. . . . . 6
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4 | 2, 3 | sylbi 199 |
. . . . 5
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5 | olc 386 |
. . . . 5
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6 | 4, 5 | syl6bi 232 |
. . . 4
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7 | ssequn2 3607 |
. . . . . 6
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8 | sseq2 3454 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | sylbi 199 |
. . . . 5
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10 | orc 387 |
. . . . 5
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11 | 9, 10 | syl6bi 232 |
. . . 4
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12 | 6, 11 | jaoi 381 |
. . 3
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13 | 1, 12 | syl 17 |
. 2
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14 | ssun 3613 |
. 2
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15 | 13, 14 | impbid1 207 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-pss 3420 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-tr 4498 df-eprel 4745 df-po 4755 df-so 4756 df-fr 4793 df-we 4795 df-ord 5426 |
This theorem is referenced by: ordsucun 6652 |
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