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Mirrors > Home > ILE Home > Th. List > morex | Unicode version |
Description: Derive membership from uniqueness. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
morex.1 |
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morex.2 |
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Ref | Expression |
---|---|
morex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 |
. . . 4
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2 | exancom 1499 |
. . . 4
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3 | 1, 2 | bitri 173 |
. . 3
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4 | nfmo1 1912 |
. . . . . 6
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5 | nfe1 1385 |
. . . . . 6
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6 | 4, 5 | nfan 1457 |
. . . . 5
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7 | mopick 1978 |
. . . . 5
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8 | 6, 7 | alrimi 1415 |
. . . 4
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9 | morex.1 |
. . . . 5
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10 | morex.2 |
. . . . . 6
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11 | eleq1 2100 |
. . . . . 6
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12 | 10, 11 | imbi12d 223 |
. . . . 5
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13 | 9, 12 | spcv 2646 |
. . . 4
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14 | 8, 13 | syl 14 |
. . 3
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15 | 3, 14 | sylan2b 271 |
. 2
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16 | 15 | ancoms 255 |
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-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 |
This theorem is referenced by: (None) |
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