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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdss | Unicode version |
Description: The inclusion of a setvar in a bounded class is a bounded formula. Note: apparently, we cannot prove from the present axioms that equality of two bounded classes is a bounded formula. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
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bdss.1 |
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Ref | Expression |
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bdss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdss.1 |
. . . 4
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2 | 1 | bdeli 9301 |
. . 3
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3 | 2 | ax-bdal 9273 |
. 2
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4 | dfss3 2929 |
. 2
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5 | 3, 4 | bd0r 9280 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-bd0 9268 ax-bdal 9273 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-ral 2305 df-in 2918 df-ss 2925 df-bdc 9296 |
This theorem is referenced by: bdeq0 9322 bdcpw 9324 bdvsn 9329 bdop 9330 bdeqsuc 9336 bj-nntrans 9411 bj-omtrans 9416 |
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