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Mirrors > Home > ILE Home > Th. List > eusvnfb | Unicode version |
Description: Two ways to say that ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eusvnfb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eusvnf 4449 |
. . 3
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2 | euex 2056 |
. . . 4
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3 | id 19 |
. . . . . . 7
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4 | vex 2740 |
. . . . . . 7
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5 | 3, 4 | eqeltrrdi 2269 |
. . . . . 6
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6 | 5 | sps 1537 |
. . . . 5
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7 | 6 | exlimiv 1598 |
. . . 4
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8 | 2, 7 | syl 14 |
. . 3
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9 | 1, 8 | jca 306 |
. 2
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10 | isset 2743 |
. . . . 5
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11 | nfcvd 2320 |
. . . . . . . 8
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12 | id 19 |
. . . . . . . 8
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13 | 11, 12 | nfeqd 2334 |
. . . . . . 7
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14 | 13 | nfrd 1520 |
. . . . . 6
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15 | 14 | eximdv 1880 |
. . . . 5
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16 | 10, 15 | biimtrid 152 |
. . . 4
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17 | 16 | imp 124 |
. . 3
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18 | eusv1 4448 |
. . 3
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19 | 17, 18 | sylibr 134 |
. 2
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20 | 9, 19 | impbii 126 |
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-ext 2159 |
This theorem depends on definitions: df-bi 117 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-v 2739 df-sbc 2963 df-csb 3058 |
This theorem is referenced by: eusv2nf 4452 eusv2 4453 |
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