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Mirrors > Home > ILE Home > Th. List > dmex | Unicode version |
Description: The domain of a set is a set. Corollary 6.8(2) of [TakeutiZaring] p. 26. (Contributed by NM, 7-Jul-2008.) |
Ref | Expression |
---|---|
dmex.1 |
Ref | Expression |
---|---|
dmex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmex.1 | . 2 | |
2 | dmexg 4852 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2128 cvv 2712 cdm 4588 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-cnv 4596 df-dm 4598 df-rn 4599 |
This theorem is referenced by: ofmres 6086 fo1st 6107 tfrlem8 6267 rdgtfr 6323 rdgruledefgg 6324 rdgon 6335 mapprc 6599 ixpprc 6666 ixpssmap2g 6674 ixpssmapg 6675 bren 6694 brdomg 6695 fundmen 6753 xpassen 6777 mapen 6793 ssenen 6798 hashfacen 10718 shftfval 10732 |
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