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Mirrors > Home > ILE Home > Th. List > dmeqd | Unicode version |
Description: Equality deduction for domain. (Contributed by NM, 4-Mar-2004.) |
Ref | Expression |
---|---|
dmeqd.1 |
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Ref | Expression |
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dmeqd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmeqd.1 |
. 2
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2 | dmeq 4839 |
. 2
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3 | 1, 2 | syl 14 |
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-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-dm 4648 |
This theorem is referenced by: rneq 4866 dmsnsnsng 5118 elxp4 5128 fndmin 5636 1stvalg 6157 fo1st 6172 f1stres 6174 errn 6571 xpassen 6844 xpdom2 6845 frecuzrdgtclt 10435 shftdm 10845 ennnfonelemg 12418 ennnfonelem1 12422 ennnfonelemhdmp1 12424 ennnfonelemkh 12427 ennnfonelemhf1o 12428 ennnfonelemex 12429 ennnfonelemhom 12430 isstruct2im 12486 isstruct2r 12487 setsvalg 12506 cnprcl2k 14002 psmetdmdm 14120 xmetdmdm 14152 blfvalps 14181 limccl 14424 ellimc3apf 14425 dvfvalap 14446 dvcj 14469 dvexp 14471 dvmptclx 14476 dvmptaddx 14477 dvmptmulx 14478 |
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