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Mirrors > Home > ILE Home > Th. List > dmss | Unicode version |
Description: Subset theorem for domain. (Contributed by NM, 11-Aug-1994.) |
Ref | Expression |
---|---|
dmss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3020 |
. . . 4
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2 | 1 | eximdv 1809 |
. . 3
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3 | vex 2623 |
. . . 4
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4 | 3 | eldm2 4647 |
. . 3
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5 | 3 | eldm2 4647 |
. . 3
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6 | 2, 4, 5 | 3imtr4g 204 |
. 2
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7 | 6 | ssrdv 3032 |
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 4461 |
This theorem is referenced by: dmeq 4649 dmv 4665 rnss 4678 dmiin 4694 dmxpss2 4876 ssxpbm 4879 ssxp1 4880 cocnvres 4968 relrelss 4970 funssxp 5193 fvun1 5383 fndmdif 5418 fneqeql2 5422 tposss 6025 smores 6071 smores2 6073 tfrlemibfn 6107 tfrlemiubacc 6109 tfr1onlembfn 6123 tfr1onlemubacc 6125 tfr1onlemres 6128 tfrcllembfn 6136 tfrcllemubacc 6138 tfrcllemres 6141 frecuzrdgtcl 9873 frecuzrdgdomlem 9878 strleund 11636 strleun 11637 |
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