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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 3161 |
. . . 4
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2 | 1 | eximdv 1890 |
. . 3
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3 | vex 2752 |
. . . 4
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4 | 3 | eldm2 4837 |
. . 3
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5 | 3 | eldm2 4837 |
. . 3
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6 | 2, 4, 5 | 3imtr4g 205 |
. 2
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7 | 6 | ssrdv 3173 |
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: dmeq 4839 dmv 4855 rnss 4869 dmiin 4885 dmxpss2 5073 ssxpbm 5076 ssxp1 5077 cocnvres 5165 relrelss 5167 funssxp 5397 fvun1 5595 fndmdif 5634 fneqeql2 5638 tposss 6261 smores 6307 smores2 6309 tfrlemibfn 6343 tfrlemiubacc 6345 tfr1onlembfn 6359 tfr1onlemubacc 6361 tfr1onlemres 6364 tfrcllembfn 6372 tfrcllemubacc 6374 tfrcllemres 6377 frecuzrdgtcl 10426 frecuzrdgdomlem 10431 ennnfonelemex 12429 strleund 12577 strleun 12578 imasaddfnlemg 12753 dvbssntrcntop 14449 |
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