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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 3963, we invoke the Axiom of Extensionality (indirectly via vtocl 2674), 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 2152 |
. . . . . 6
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3 | 2 | anbi1d 454 |
. . . . 5
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4 | 3 | bibi2d 231 |
. . . 4
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5 | 4 | albidv 1753 |
. . 3
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6 | 5 | exbidv 1754 |
. 2
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7 | ax-sep 3963 |
. 2
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8 | 1, 6, 7 | vtocl 2674 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-ext 2071 ax-sep 3963 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-v 2622 |
This theorem is referenced by: inex1 3979 bj-d0clsepcl 12093 |
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