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Mirrors > Home > ILE Home > Th. List > relrelss | Unicode version |
Description: Two ways to describe the structure of a two-place operation. (Contributed by NM, 17-Dec-2008.) |
Ref | Expression |
---|---|
relrelss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel 4632 |
. . 3
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2 | 1 | anbi2i 457 |
. 2
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3 | relssdmrn 5148 |
. . . 4
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4 | ssv 3177 |
. . . . 5
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5 | xpss12 4732 |
. . . . 5
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6 | 4, 5 | mpan2 425 |
. . . 4
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7 | 3, 6 | sylan9ss 3168 |
. . 3
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8 | xpss 4733 |
. . . . . 6
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9 | sstr 3163 |
. . . . . 6
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10 | 8, 9 | mpan2 425 |
. . . . 5
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11 | df-rel 4632 |
. . . . 5
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12 | 10, 11 | sylibr 134 |
. . . 4
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13 | dmss 4825 |
. . . . 5
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14 | vn0m 3434 |
. . . . . 6
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15 | dmxpm 4846 |
. . . . . 6
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16 | 14, 15 | ax-mp 5 |
. . . . 5
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17 | 13, 16 | sseqtrdi 3203 |
. . . 4
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18 | 12, 17 | jca 306 |
. . 3
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19 | 7, 18 | impbii 126 |
. 2
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20 | 2, 19 | bitri 184 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-br 4003 df-opab 4064 df-xp 4631 df-rel 4632 df-cnv 4633 df-dm 4635 df-rn 4636 |
This theorem is referenced by: dftpos3 6260 tpostpos2 6263 |
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