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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 3164 |
. . . 4
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2 | ssel 3164 |
. . . 4
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3 | 1, 2 | im2anan9 598 |
. . 3
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4 | 3 | ssopab2dv 4296 |
. 2
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5 | df-xp 4650 |
. 2
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6 | df-xp 4650 |
. 2
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7 | 4, 5, 6 | 3sstr4g 3213 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-in 3150 df-ss 3157 df-opab 4080 df-xp 4650 |
This theorem is referenced by: xpss 4752 xpss1 4754 xpss2 4755 djussxp 4790 ssxpbm 5082 ssrnres 5089 cossxp 5169 cossxp2 5170 cocnvss 5172 relrelss 5173 fssxp 5402 oprabss 5983 pmss12g 6702 caserel 7117 casef 7118 dmaddpi 7355 dmmulpi 7356 rexpssxrxp 8033 ltrelxr 8049 dfz2 9356 phimullem 12260 txuni2 14233 txbas 14235 neitx 14245 txcnp 14248 cnmpt2res 14274 psmetres2 14310 xmetres2 14356 metres2 14358 xmetresbl 14417 xmettx 14487 qtopbasss 14498 tgqioo 14524 resubmet 14525 limccnp2lem 14622 limccnp2cntop 14623 |
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