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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 4798 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2681 cdm 4534 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-cnv 4542 df-dm 4544 df-rn 4545 |
This theorem is referenced by: ofmres 6027 fo1st 6048 tfrlem8 6208 rdgtfr 6264 rdgruledefgg 6265 rdgon 6276 mapprc 6539 ixpprc 6606 ixpssmap2g 6614 ixpssmapg 6615 bren 6634 brdomg 6635 fundmen 6693 xpassen 6717 mapen 6733 ssenen 6738 hashfacen 10572 shftfval 10586 |
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