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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3055 |
. . . 4
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2 | ssel 3055 |
. . . 4
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3 | 1, 2 | im2anan9 570 |
. . 3
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4 | 3 | ssopab2dv 4158 |
. 2
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5 | df-xp 4503 |
. 2
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6 | df-xp 4503 |
. 2
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7 | 4, 5, 6 | 3sstr4g 3104 |
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-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-in 3041 df-ss 3048 df-opab 3948 df-xp 4503 |
This theorem is referenced by: xpss 4605 xpss1 4607 xpss2 4608 djussxp 4642 ssxpbm 4930 ssrnres 4937 cossxp 5017 cossxp2 5018 cocnvss 5020 relrelss 5021 fssxp 5246 oprabss 5809 pmss12g 6521 caserel 6922 casef 6923 dmaddpi 7075 dmmulpi 7076 rexpssxrxp 7728 ltrelxr 7743 dfz2 9021 phimullem 11740 txuni2 12261 txbas 12263 neitx 12273 txcnp 12276 cnmpt2res 12302 psmetres2 12316 xmetres2 12362 metres2 12364 xmetresbl 12423 xmettx 12493 qtopbasss 12504 tgqioo 12527 resubmet 12528 limccnp2lem 12595 limccnp2cntop 12596 |
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