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Mirrors > Home > ILE Home > Th. List > suplub2ti | Unicode version |
Description: Bidirectional form of suplubti 7030. (Contributed by Jim Kingdon, 17-Jan-2022.) |
Ref | Expression |
---|---|
supmoti.ti |
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supclti.2 |
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suplub2ti.or |
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suplub2ti.3 |
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Ref | Expression |
---|---|
suplub2ti |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supmoti.ti |
. . . 4
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2 | supclti.2 |
. . . 4
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3 | 1, 2 | suplubti 7030 |
. . 3
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4 | 3 | expdimp 259 |
. 2
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5 | breq2 4022 |
. . . 4
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6 | 5 | cbvrexv 2719 |
. . 3
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7 | simplll 533 |
. . . . . . 7
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8 | simplr 528 |
. . . . . . 7
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9 | 1, 2 | supubti 7029 |
. . . . . . 7
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10 | 7, 8, 9 | sylc 62 |
. . . . . 6
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11 | simpr 110 |
. . . . . . 7
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12 | suplub2ti.or |
. . . . . . . . 9
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13 | 12 | ad3antrrr 492 |
. . . . . . . 8
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14 | simpllr 534 |
. . . . . . . 8
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15 | suplub2ti.3 |
. . . . . . . . . 10
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16 | 15 | ad3antrrr 492 |
. . . . . . . . 9
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17 | 16, 8 | sseldd 3171 |
. . . . . . . 8
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18 | 1, 2 | supclti 7028 |
. . . . . . . . 9
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19 | 18 | ad3antrrr 492 |
. . . . . . . 8
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20 | sowlin 4338 |
. . . . . . . 8
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21 | 13, 14, 17, 19, 20 | syl13anc 1251 |
. . . . . . 7
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22 | 11, 21 | mpd 13 |
. . . . . 6
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23 | 10, 22 | ecased 1360 |
. . . . 5
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24 | 23 | ex 115 |
. . . 4
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25 | 24 | rexlimdva 2607 |
. . 3
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26 | 6, 25 | biimtrid 152 |
. 2
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27 | 4, 26 | impbid 129 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-reu 2475 df-rmo 2476 df-rab 2477 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-iso 4315 df-iota 5196 df-riota 5852 df-sup 7014 |
This theorem is referenced by: suprlubex 8940 |
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