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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 15338 |
. . 3
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3 | 2 | ax-bdal 15310 |
. 2
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4 | dfss3 3169 |
. 2
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5 | 3, 4 | bd0r 15317 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 ax-bd0 15305 ax-bdal 15310 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-ral 2477 df-in 3159 df-ss 3166 df-bdc 15333 |
This theorem is referenced by: bdeq0 15359 bdcpw 15361 bdvsn 15366 bdop 15367 bdeqsuc 15373 bj-nntrans 15443 bj-omtrans 15448 |
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