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Mirrors > Home > ILE Home > Th. List > ralxpf | Unicode version |
Description: Version of ralxp 4690 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 2671 |
. 2
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2 | cbvralsv 2671 |
. . . 4
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3 | 2 | ralbii 2444 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | nfv 1509 |
. . . 4
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5 | nfcv 2282 |
. . . . 5
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6 | nfs1v 1913 |
. . . . 5
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7 | 5, 6 | nfralxy 2474 |
. . . 4
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8 | sbequ12 1745 |
. . . . 5
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9 | 8 | ralbidv 2438 |
. . . 4
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10 | 4, 7, 9 | cbvral 2653 |
. . 3
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11 | vex 2692 |
. . . . . 6
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12 | vex 2692 |
. . . . . 6
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13 | 11, 12 | eqvinop 4173 |
. . . . 5
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14 | ralxpf.1 |
. . . . . . . 8
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15 | 14 | nfsb 1920 |
. . . . . . 7
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16 | 6 | nfsb 1920 |
. . . . . . 7
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17 | 15, 16 | nfbi 1569 |
. . . . . 6
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18 | ralxpf.2 |
. . . . . . . . 9
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19 | 18 | nfsb 1920 |
. . . . . . . 8
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20 | nfs1v 1913 |
. . . . . . . 8
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21 | 19, 20 | nfbi 1569 |
. . . . . . 7
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22 | ralxpf.3 |
. . . . . . . . 9
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23 | ralxpf.4 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 22, 23 | sbhypf 2738 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | vex 2692 |
. . . . . . . . . 10
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26 | vex 2692 |
. . . . . . . . . 10
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27 | 25, 26 | opth 4167 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | sbequ12 1745 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 8, 28 | sylan9bb 458 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 27, 29 | sylbi 120 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 24, 30 | sylan9bb 458 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 21, 31 | exlimi 1574 |
. . . . . 6
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33 | 17, 32 | exlimi 1574 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 13, 33 | sylbi 120 |
. . . 4
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35 | 34 | ralxp 4690 |
. . 3
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36 | 3, 10, 35 | 3bitr4ri 212 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
37 | 1, 36 | bitri 183 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
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-sbc 2914 df-csb 3008 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-iun 3823 df-opab 3998 df-xp 4553 df-rel 4554 |
This theorem is referenced by: (None) |
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