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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4479 with bound-variable hypotheses. (Contributed by NM, 18-Aug-2006.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
ralxpf.1 |
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ralxpf.2 |
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ralxpf.3 |
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ralxpf.4 |
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Ref | Expression |
---|---|
ralxpf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 2544 |
. 2
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2 | cbvralsv 2544 |
. . . 4
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3 | 2 | ralbii 2330 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | nfv 1421 |
. . . 4
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5 | nfcv 2178 |
. . . . 5
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6 | nfs1v 1815 |
. . . . 5
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7 | 5, 6 | nfralxy 2360 |
. . . 4
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8 | sbequ12 1654 |
. . . . 5
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9 | 8 | ralbidv 2326 |
. . . 4
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10 | 4, 7, 9 | cbvral 2529 |
. . 3
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11 | vex 2560 |
. . . . . 6
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12 | vex 2560 |
. . . . . 6
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13 | 11, 12 | eqvinop 3980 |
. . . . 5
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14 | ralxpf.1 |
. . . . . . . 8
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15 | 14 | nfsb 1822 |
. . . . . . 7
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16 | 6 | nfsb 1822 |
. . . . . . 7
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17 | 15, 16 | nfbi 1481 |
. . . . . 6
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18 | ralxpf.2 |
. . . . . . . . 9
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19 | 18 | nfsb 1822 |
. . . . . . . 8
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20 | nfs1v 1815 |
. . . . . . . 8
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21 | 19, 20 | nfbi 1481 |
. . . . . . 7
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22 | ralxpf.3 |
. . . . . . . . 9
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23 | ralxpf.4 |
. . . . . . . . 9
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24 | 22, 23 | sbhypf 2603 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | vex 2560 |
. . . . . . . . . 10
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26 | vex 2560 |
. . . . . . . . . 10
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27 | 25, 26 | opth 3974 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | sbequ12 1654 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 8, 28 | sylan9bb 435 |
. . . . . . . . 9
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30 | 27, 29 | sylbi 114 |
. . . . . . . 8
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31 | 24, 30 | sylan9bb 435 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 21, 31 | exlimi 1485 |
. . . . . 6
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33 | 17, 32 | exlimi 1485 |
. . . . 5
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34 | 13, 33 | sylbi 114 |
. . . 4
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35 | 34 | ralxp 4479 |
. . 3
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36 | 3, 10, 35 | 3bitr4ri 202 |
. 2
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37 | 1, 36 | bitri 173 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-iun 3659 df-opab 3819 df-xp 4351 df-rel 4352 |
This theorem is referenced by: (None) |
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