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Mirrors > Home > ILE Home > Th. List > zfauscl | Unicode version |
Description: Separation Scheme (Aussonderung) using a class variable. To derive this from ax-sep 4133, we invoke the Axiom of Extensionality (indirectly via vtocl 2803), which is needed for the justification of class variable notation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
zfauscl.1 |
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Ref | Expression |
---|---|
zfauscl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfauscl.1 |
. 2
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2 | eleq2 2251 |
. . . . . 6
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3 | 2 | anbi1d 465 |
. . . . 5
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4 | 3 | bibi2d 232 |
. . . 4
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5 | 4 | albidv 1834 |
. . 3
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6 | 5 | exbidv 1835 |
. 2
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7 | ax-sep 4133 |
. 2
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8 | 1, 6, 7 | vtocl 2803 |
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 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-ext 2169 ax-sep 4133 |
This theorem depends on definitions: df-bi 117 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-v 2751 |
This theorem is referenced by: inex1 4149 bj-d0clsepcl 14973 |
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