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Mirrors > Home > ILE Home > Th. List > eqimssi | Unicode version |
Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.) |
Ref | Expression |
---|---|
eqimssi.1 |
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Ref | Expression |
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eqimssi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3122 |
. 2
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2 | eqimssi.1 |
. 2
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3 | 1, 2 | sseqtri 3136 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-in 3082 df-ss 3089 |
This theorem is referenced by: funi 5163 fpr 5610 elfzo1 9998 sumsplitdc 11233 isumlessdc 11297 |
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