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Mirrors > Home > ILE Home > Th. List > omexg | Unicode version |
Description: Ordinal multiplication is a set. (Contributed by Mario Carneiro, 3-Jul-2019.) |
Ref | Expression |
---|---|
omexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2712 |
. . . 4
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2 | 0ex 4087 |
. . . . 5
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3 | vex 2712 |
. . . . . 6
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4 | omfnex 6385 |
. . . . . 6
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5 | 3, 4 | ax-mp 5 |
. . . . 5
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6 | 2, 5 | rdgexg 6326 |
. . . 4
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7 | 1, 6 | ax-mp 5 |
. . 3
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8 | 7 | gen2 1427 |
. 2
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9 | df-omul 6358 |
. . 3
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10 | 9 | mpofvex 6141 |
. 2
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11 | 8, 10 | mp3an1 1303 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-13 2127 ax-14 2128 ax-ext 2136 ax-coll 4075 ax-sep 4078 ax-nul 4086 ax-pow 4130 ax-pr 4164 ax-un 4388 ax-setind 4490 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1740 df-eu 2006 df-mo 2007 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ne 2325 df-ral 2437 df-rex 2438 df-reu 2439 df-rab 2441 df-v 2711 df-sbc 2934 df-csb 3028 df-dif 3100 df-un 3102 df-in 3104 df-ss 3111 df-nul 3391 df-pw 3541 df-sn 3562 df-pr 3563 df-op 3565 df-uni 3769 df-iun 3847 df-br 3962 df-opab 4022 df-mpt 4023 df-tr 4059 df-id 4248 df-iord 4321 df-on 4323 df-suc 4326 df-xp 4585 df-rel 4586 df-cnv 4587 df-co 4588 df-dm 4589 df-rn 4590 df-res 4591 df-ima 4592 df-iota 5128 df-fun 5165 df-fn 5166 df-f 5167 df-f1 5168 df-fo 5169 df-f1o 5170 df-fv 5171 df-ov 5817 df-oprab 5818 df-mpo 5819 df-1st 6078 df-2nd 6079 df-recs 6242 df-irdg 6307 df-oadd 6357 df-omul 6358 |
This theorem is referenced by: fnoei 6388 oeiexg 6389 oeiv 6392 omv2 6401 |
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