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Mirrors > Home > ILE Home > Th. List > dmxpid | Unicode version |
Description: The domain of a square Cartesian product. (Contributed by NM, 28-Jul-1995.) (Revised by Jim Kingdon, 11-Apr-2023.) |
Ref | Expression |
---|---|
dmxpid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xp 4503 |
. . 3
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2 | 1 | dmeqi 4698 |
. 2
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3 | elex2 2671 |
. . . 4
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4 | 3 | rgen 2457 |
. . 3
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5 | dmopab3 4710 |
. . 3
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6 | 4, 5 | mpbi 144 |
. 2
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7 | 2, 6 | eqtri 2133 |
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 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-v 2657 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-br 3894 df-opab 3948 df-xp 4503 df-dm 4507 |
This theorem is referenced by: dmxpin 4719 xpid11 4720 sqxpeq0 4918 xpider 6452 psmetdmdm 12307 xmetdmdm 12339 |
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