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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 2355 |
. . . 4
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2 | exancom 1540 |
. . . 4
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3 | 1, 2 | bitri 182 |
. . 3
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4 | nfmo1 1954 |
. . . . . 6
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5 | nfe1 1426 |
. . . . . 6
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6 | 4, 5 | nfan 1498 |
. . . . 5
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7 | mopick 2020 |
. . . . 5
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8 | 6, 7 | alrimi 1456 |
. . . 4
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9 | morex.1 |
. . . . 5
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10 | morex.2 |
. . . . . 6
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11 | eleq1 2142 |
. . . . . 6
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12 | 10, 11 | imbi12d 232 |
. . . . 5
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13 | 9, 12 | spcv 2692 |
. . . 4
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14 | 8, 13 | syl 14 |
. . 3
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15 | 3, 14 | sylan2b 281 |
. 2
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16 | 15 | ancoms 264 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-eu 1945 df-mo 1946 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-rex 2355 df-v 2604 |
This theorem is referenced by: (None) |
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