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Mirrors > Home > ILE Home > Th. List > xpss12 | Unicode version |
Description: Subset theorem for cross product. Generalization of Theorem 101 of [Suppes] p. 52. (Contributed by NM, 26-Aug-1995.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
xpss12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3086 | . . . 4 | |
2 | ssel 3086 | . . . 4 | |
3 | 1, 2 | im2anan9 587 | . . 3 |
4 | 3 | ssopab2dv 4195 | . 2 |
5 | df-xp 4540 | . 2 | |
6 | df-xp 4540 | . 2 | |
7 | 4, 5, 6 | 3sstr4g 3135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 wss 3066 copab 3983 cxp 4532 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-in 3072 df-ss 3079 df-opab 3985 df-xp 4540 |
This theorem is referenced by: xpss 4642 xpss1 4644 xpss2 4645 djussxp 4679 ssxpbm 4969 ssrnres 4976 cossxp 5056 cossxp2 5057 cocnvss 5059 relrelss 5060 fssxp 5285 oprabss 5850 pmss12g 6562 caserel 6965 casef 6966 dmaddpi 7126 dmmulpi 7127 rexpssxrxp 7803 ltrelxr 7818 dfz2 9116 phimullem 11890 txuni2 12414 txbas 12416 neitx 12426 txcnp 12429 cnmpt2res 12455 psmetres2 12491 xmetres2 12537 metres2 12539 xmetresbl 12598 xmettx 12668 qtopbasss 12679 tgqioo 12705 resubmet 12706 limccnp2lem 12803 limccnp2cntop 12804 |
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