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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sels | Unicode version |
Description: If a class is a set, then it is a member of a set. (Copied from set.mm.) (Contributed by BJ, 3-Apr-2019.) |
Ref | Expression |
---|---|
bj-sels |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 3621 |
. . 3
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2 | bj-snexg 14546 |
. . . . 5
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3 | sbcel2g 3078 |
. . . . 5
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4 | 2, 3 | syl 14 |
. . . 4
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5 | csbvarg 3085 |
. . . . . 6
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6 | 2, 5 | syl 14 |
. . . . 5
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7 | 6 | eleq2d 2247 |
. . . 4
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8 | 4, 7 | bitrd 188 |
. . 3
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9 | 1, 8 | mpbird 167 |
. 2
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10 | 9 | spesbcd 3049 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-pr 4209 ax-bdor 14450 ax-bdeq 14454 ax-bdsep 14518 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-sbc 2963 df-csb 3058 df-un 3133 df-sn 3598 df-pr 3599 |
This theorem is referenced by: (None) |
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