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Mirrors > Home > ILE Home > Th. List > elintab | Unicode version |
Description: Membership in the intersection of a class abstraction. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
inteqab.1 |
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Ref | Expression |
---|---|
elintab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqab.1 |
. . 3
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2 | 1 | elint 3809 |
. 2
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3 | nfsab1 2144 |
. . . 4
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4 | nfv 1505 |
. . . 4
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5 | 3, 4 | nfim 1549 |
. . 3
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6 | nfv 1505 |
. . 3
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7 | eleq1 2217 |
. . . . 5
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8 | abid 2142 |
. . . . 5
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9 | 7, 8 | bitrdi 195 |
. . . 4
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10 | eleq2 2218 |
. . . 4
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11 | 9, 10 | imbi12d 233 |
. . 3
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12 | 5, 6, 11 | cbval 1731 |
. 2
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13 | 2, 12 | bitri 183 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-v 2711 df-int 3804 |
This theorem is referenced by: elintrab 3815 intmin4 3831 intab 3832 intid 4179 |
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