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Mirrors > Home > ILE Home > Th. List > onun2 | Unicode version |
Description: The union of two ordinal numbers is an ordinal number. (Contributed by Jim Kingdon, 25-Jul-2019.) |
Ref | Expression |
---|---|
onun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prssi 3686 |
. 2
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2 | prexg 4141 |
. . . 4
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3 | ssonuni 4412 |
. . . 4
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4 | 2, 3 | syl 14 |
. . 3
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5 | uniprg 3759 |
. . . 4
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6 | 5 | eleq1d 2209 |
. . 3
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7 | 4, 6 | sylibd 148 |
. 2
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8 | 1, 7 | mpd 13 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-uni 3745 df-tr 4035 df-iord 4296 df-on 4298 |
This theorem is referenced by: onun2i 4415 rdgon 6291 |
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