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Mirrors > Home > ILE Home > Th. List > dmexg | Unicode version |
Description: The domain of a set is a set. Corollary 6.8(2) of [TakeutiZaring] p. 26. (Contributed by NM, 7-Apr-1995.) |
Ref | Expression |
---|---|
dmexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniexg 4460 |
. 2
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2 | uniexg 4460 |
. 2
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3 | ssun1 3313 |
. . . 4
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4 | dmrnssfld 4911 |
. . . 4
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5 | 3, 4 | sstri 3179 |
. . 3
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6 | ssexg 4160 |
. . 3
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7 | 5, 6 | mpan 424 |
. 2
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8 | 1, 2, 7 | 3syl 17 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 ax-un 4454 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-br 4022 df-opab 4083 df-cnv 4655 df-dm 4657 df-rn 4658 |
This theorem is referenced by: dmex 4914 iprc 4916 exse2 5023 xpexr2m 5091 elxp4 5137 cnvexg 5187 coexg 5194 dmfex 5427 cofunexg 6138 offval3 6163 1stvalg 6171 tposexg 6287 erexb 6588 f1vrnfibi 6978 shftfvalg 10868 ennnfonelemp1 12468 ptex 12780 prdsex 12785 xmetunirn 14343 |
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