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Mirrors > Home > ILE Home > Th. List > clelab | Unicode version |
Description: Membership of a class variable in a class abstraction. (Contributed by NM, 23-Dec-1993.) |
Ref | Expression |
---|---|
clelab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clab 2164 |
. . . 4
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2 | 1 | anbi2i 457 |
. . 3
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3 | 2 | exbii 1605 |
. 2
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4 | df-clel 2173 |
. 2
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5 | nfv 1528 |
. . 3
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6 | nfv 1528 |
. . . 4
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7 | nfs1v 1939 |
. . . 4
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8 | 6, 7 | nfan 1565 |
. . 3
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9 | eqeq1 2184 |
. . . 4
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10 | sbequ12 1771 |
. . . 4
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11 | 9, 10 | anbi12d 473 |
. . 3
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12 | 5, 8, 11 | cbvex 1756 |
. 2
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13 | 3, 4, 12 | 3bitr4i 212 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 |
This theorem is referenced by: elrabi 2890 |
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