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Mirrors > Home > ILE Home > Th. List > ipsbased | Unicode version |
Description: The base set of a constructed inner product space. (Contributed by Stefan O'Rear, 27-Nov-2014.) (Revised by Jim Kingdon, 7-Feb-2023.) |
Ref | Expression |
---|---|
ipspart.a |
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ipsstrd.b |
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ipsstrd.p |
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ipsstrd.r |
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ipsstrd.s |
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ipsstrd.x |
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ipsstrd.i |
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Ref | Expression |
---|---|
ipsbased |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ipspart.a |
. . 3
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2 | ipsstrd.b |
. . 3
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3 | ipsstrd.p |
. . 3
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4 | ipsstrd.r |
. . 3
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5 | ipsstrd.s |
. . 3
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6 | ipsstrd.x |
. . 3
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7 | ipsstrd.i |
. . 3
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8 | 1, 2, 3, 4, 5, 6, 7 | ipsstrd 12698 |
. 2
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9 | basendxnn 12579 |
. . . . 5
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10 | opexg 4249 |
. . . . 5
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11 | 9, 2, 10 | sylancr 414 |
. . . 4
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12 | tpid1g 3722 |
. . . 4
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13 | elun1 3317 |
. . . 4
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14 | 11, 12, 13 | 3syl 17 |
. . 3
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15 | 14, 1 | eleqtrrdi 2283 |
. 2
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16 | 8, 2, 15 | opelstrbas 12638 |
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-in1 615 ax-in2 616 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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 ax-un 4454 ax-setind 4557 ax-cnex 7937 ax-resscn 7938 ax-1cn 7939 ax-1re 7940 ax-icn 7941 ax-addcl 7942 ax-addrcl 7943 ax-mulcl 7944 ax-addcom 7946 ax-addass 7948 ax-distr 7950 ax-i2m1 7951 ax-0lt1 7952 ax-0id 7954 ax-rnegex 7955 ax-cnre 7957 ax-pre-ltirr 7958 ax-pre-ltwlin 7959 ax-pre-lttrn 7960 ax-pre-apti 7961 ax-pre-ltadd 7962 |
This theorem depends on definitions: df-bi 117 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3595 df-sn 3616 df-pr 3617 df-tp 3618 df-op 3619 df-uni 3828 df-int 3863 df-br 4022 df-opab 4083 df-mpt 4084 df-id 4314 df-xp 4653 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-rn 4658 df-res 4659 df-ima 4660 df-iota 5199 df-fun 5240 df-fn 5241 df-f 5242 df-fv 5246 df-riota 5855 df-ov 5903 df-oprab 5904 df-mpo 5905 df-pnf 8029 df-mnf 8030 df-xr 8031 df-ltxr 8032 df-le 8033 df-sub 8165 df-neg 8166 df-inn 8955 df-2 9013 df-3 9014 df-4 9015 df-5 9016 df-6 9017 df-7 9018 df-8 9019 df-n0 9212 df-z 9289 df-uz 9564 df-fz 10045 df-struct 12525 df-ndx 12526 df-slot 12527 df-base 12529 df-plusg 12613 df-mulr 12614 df-sca 12616 df-vsca 12617 df-ip 12618 |
This theorem is referenced by: (None) |
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