Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > xpexg | Unicode version |
Description: The cross product of two sets is a set. Proposition 6.2 of [TakeutiZaring] p. 23. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
xpexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpsspw 4651 | . 2 | |
2 | unexg 4364 | . . 3 | |
3 | pwexg 4104 | . . 3 | |
4 | pwexg 4104 | . . 3 | |
5 | 2, 3, 4 | 3syl 17 | . 2 |
6 | ssexg 4067 | . 2 | |
7 | 1, 5, 6 | sylancr 410 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 cvv 2686 cun 3069 wss 3071 cpw 3510 cxp 4537 |
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 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-opab 3990 df-xp 4545 |
This theorem is referenced by: xpex 4654 sqxpexg 4655 resiexg 4864 cnvexg 5076 coexg 5083 fex2 5291 fabexg 5310 resfunexgALT 6008 cofunexg 6009 fnexALT 6011 opabex3d 6019 opabex3 6020 oprabexd 6025 ofmresex 6035 mpoexxg 6108 tposexg 6155 erex 6453 pmex 6547 mapex 6548 pmvalg 6553 elpmg 6558 fvdiagfn 6587 ixpexgg 6616 ixpsnf1o 6630 map1 6706 xpdom2 6725 xpdom3m 6728 xpen 6739 mapxpen 6742 xpfi 6818 djuex 6928 djuassen 7073 shftfvalg 10590 climconst2 11060 lmfval 12361 txbasex 12426 txopn 12434 txcn 12444 txrest 12445 blfvalps 12554 xmetxp 12676 limccnp2lem 12814 limccnp2cntop 12815 dvfvalap 12819 |
Copyright terms: Public domain | W3C validator |