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Mirrors > Home > ILE Home > Th. List > hbae | Unicode version |
Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
hbae |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12or 1403 |
. . . 4
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2 | ax10o 1603 |
. . . . . 6
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3 | 2 | alequcoms 1409 |
. . . . 5
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4 | ax10o 1603 |
. . . . . . . . 9
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5 | 4 | pm2.43i 43 |
. . . . . . . 8
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6 | ax10o 1603 |
. . . . . . . 8
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7 | 5, 6 | syl5 28 |
. . . . . . 7
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8 | 7 | alequcoms 1409 |
. . . . . 6
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9 | ax-4 1400 |
. . . . . . . 8
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10 | 9 | imim1i 54 |
. . . . . . 7
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11 | 10 | sps 1430 |
. . . . . 6
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12 | 8, 11 | jaoi 636 |
. . . . 5
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13 | 3, 12 | jaoi 636 |
. . . 4
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14 | 1, 13 | ax-mp 7 |
. . 3
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15 | 14 | a5i 1435 |
. 2
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16 | ax-7 1337 |
. 2
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17 | 15, 16 | syl 14 |
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-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: nfae 1607 hbaes 1608 hbnae 1609 dral1 1618 dral2 1619 drex2 1620 drex1 1679 aev 1693 sbcomxyyz 1846 exists1 1996 |
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