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Mirrors > Home > MPE Home > Th. List > xpsn | Structured version Visualization version Unicode version |
Description: The Cartesian product of two singletons. (Contributed by NM, 4-Nov-2006.) |
Ref | Expression |
---|---|
xpsn.1 | |
xpsn.2 |
Ref | Expression |
---|---|
xpsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpsn.1 | . 2 | |
2 | xpsn.2 | . 2 | |
3 | xpsng 6406 | . 2 | |
4 | 1, 2, 3 | mp2an 708 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wcel 1990 cvv 3200 csn 4177 cop 4183 cxp 5112 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 |
This theorem is referenced by: dfmpt 6410 fpar 7281 mapsnconst 7903 ixpsnf1o 7948 cda1dif 8998 infcda1 9015 s1co 13579 xpsc0 16220 xpsc1 16221 mat1f1o 20284 txdis 21435 pt1hmeo 21609 utop2nei 22054 utop3cls 22055 imasdsf1olem 22178 ex-xp 27293 poimirlem3 33412 poimirlem4 33413 poimirlem9 33418 poimirlem28 33437 grposnOLD 33681 dib0 36453 |
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