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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 2938 |
. 2
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3 | df-br 3756 |
. 2
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4 | df-br 3756 |
. 2
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5 | 2, 3, 4 | 3imtr4g 194 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-in 2918 df-ss 2925 df-br 3756 |
This theorem is referenced by: ssbri 3797 sess1 4059 brrelex12 4324 coss1 4434 coss2 4435 eqbrrdva 4448 ersym 6054 ertr 6057 |
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