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Mirrors > Home > ILE Home > Th. List > ssbrd | Unicode version |
Description: Deduction from a subclass relationship of binary relations. (Contributed by NM, 30-Apr-2004.) |
Ref | Expression |
---|---|
ssbrd.1 |
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Ref | Expression |
---|---|
ssbrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssbrd.1 |
. . 3
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2 | 1 | sseld 3060 |
. 2
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3 | df-br 3894 |
. 2
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4 | df-br 3894 |
. 2
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5 | 2, 3, 4 | 3imtr4g 204 |
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-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-11 1465 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-in 3041 df-ss 3048 df-br 3894 |
This theorem is referenced by: ssbri 3935 sess1 4217 brrelex12 4535 coss1 4652 coss2 4653 eqbrrdva 4667 ersym 6393 ertr 6396 |
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