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Mirrors > Home > ILE Home > Th. List > opex | Unicode version |
Description: An ordered pair of sets is a set. (Contributed by Jim Kingdon, 24-Sep-2018.) (Revised by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
opex.1 |
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opex.2 |
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Ref | Expression |
---|---|
opex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex.1 |
. 2
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2 | opex.2 |
. 2
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3 | opexg 4066 |
. 2
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4 | 1, 2, 3 | mp2an 418 |
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-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3965 ax-pow 4017 ax-pr 4047 |
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 2624 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 |
This theorem is referenced by: otth2 4079 opabid 4095 elopab 4096 opabm 4118 elvvv 4516 relsnop 4559 xpiindim 4588 raliunxp 4592 rexiunxp 4593 intirr 4833 xpmlem 4867 dmsnm 4911 dmsnopg 4917 cnvcnvsn 4922 op2ndb 4929 cnviinm 4987 funopg 5063 fsn 5485 fvsn 5508 idref 5552 oprabid 5697 dfoprab2 5712 rnoprab 5747 fo1st 5944 fo2nd 5945 eloprabi 5982 xporderlem 6012 cnvoprab 6015 dmtpos 6037 rntpos 6038 tpostpos 6045 iinerm 6380 th3qlem2 6411 elixpsn 6508 ensn1 6569 mapsnen 6584 xpsnen 6593 xpcomco 6598 xpassen 6602 xpmapenlem 6621 phplem2 6625 ac6sfi 6670 djuss 6817 genipdm 7138 ioof 9452 fsumcnv 10894 |
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