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Mirrors > Home > ILE Home > Th. List > suplub2ti | Unicode version |
Description: Bidirectional form of suplubti 6775. (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 6775 |
. . 3
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4 | 3 | expdimp 256 |
. 2
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5 | breq2 3871 |
. . . 4
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6 | 5 | cbvrexv 2605 |
. . 3
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7 | simplll 501 |
. . . . . . 7
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8 | simplr 498 |
. . . . . . 7
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9 | 1, 2 | supubti 6774 |
. . . . . . 7
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10 | 7, 8, 9 | sylc 62 |
. . . . . 6
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11 | simpr 109 |
. . . . . . 7
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12 | suplub2ti.or |
. . . . . . . . 9
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13 | 12 | ad3antrrr 477 |
. . . . . . . 8
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14 | simpllr 502 |
. . . . . . . 8
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15 | suplub2ti.3 |
. . . . . . . . . 10
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16 | 15 | ad3antrrr 477 |
. . . . . . . . 9
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17 | 16, 8 | sseldd 3040 |
. . . . . . . 8
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18 | 1, 2 | supclti 6773 |
. . . . . . . . 9
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19 | 18 | ad3antrrr 477 |
. . . . . . . 8
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20 | sowlin 4171 |
. . . . . . . 8
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21 | 13, 14, 17, 19, 20 | syl13anc 1183 |
. . . . . . 7
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22 | 11, 21 | mpd 13 |
. . . . . 6
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23 | 10, 22 | ecased 1292 |
. . . . 5
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24 | 23 | ex 114 |
. . . 4
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25 | 24 | rexlimdva 2502 |
. . 3
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26 | 6, 25 | syl5bi 151 |
. 2
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27 | 4, 26 | impbid 128 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-reu 2377 df-rmo 2378 df-rab 2379 df-v 2635 df-sbc 2855 df-un 3017 df-in 3019 df-ss 3026 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-iso 4148 df-iota 5014 df-riota 5646 df-sup 6759 |
This theorem is referenced by: suprlubex 8510 |
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