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Mirrors > Home > ILE Home > Th. List > abnex | Unicode version |
Description: Sufficient condition for a class abstraction to be a proper class. Lemma for snnex 4307 and pwnex 4308. See the comment of abnexg 4305. (Contributed by BJ, 2-May-2021.) |
Ref | Expression |
---|---|
abnex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vprc 4000 |
. 2
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2 | alral 2437 |
. . 3
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3 | rexv 2659 |
. . . . . . 7
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4 | 3 | bicomi 131 |
. . . . . 6
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5 | 4 | abbii 2215 |
. . . . 5
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6 | 5 | eleq1i 2165 |
. . . 4
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7 | 6 | biimpi 119 |
. . 3
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8 | abnexg 4305 |
. . 3
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9 | 2, 7, 8 | syl2im 38 |
. 2
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10 | 1, 9 | mtoi 631 |
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-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-un 4293 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-in 3027 df-ss 3034 df-sn 3480 df-uni 3684 df-iun 3762 |
This theorem is referenced by: pwnex 4308 |
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