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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 4649 |
. 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-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-dm 4462 |
This theorem is referenced by: rneq 4675 dmsnsnsng 4921 elxp4 4931 fndmin 5420 1stvalg 5927 fo1st 5942 f1stres 5944 errn 6328 xpassen 6600 xpdom2 6601 frecuzrdgtclt 9889 shftdm 10317 isstruct2im 11565 isstruct2r 11566 setsvalg 11585 |
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