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Mirrors > Home > ILE Home > Th. List > strndxid | Unicode version |
Description: The value of a structure component extractor is the value of the corresponding slot of the structure. (Contributed by AV, 13-Mar-2020.) |
Ref | Expression |
---|---|
strndxid.s |
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strndxid.e |
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strndxid.n |
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Ref | Expression |
---|---|
strndxid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strndxid.e |
. . . 4
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2 | strndxid.n |
. . . 4
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3 | 1, 2 | ndxid 12536 |
. . 3
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4 | strndxid.s |
. . 3
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5 | 1, 2 | ndxarg 12535 |
. . . . 5
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6 | 5, 2 | eqeltri 2262 |
. . . 4
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7 | 6 | a1i 9 |
. . 3
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8 | 3, 4, 7 | strnfvnd 12532 |
. 2
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9 | 8 | eqcomd 2195 |
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-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-cnex 7932 ax-resscn 7933 ax-1re 7935 ax-addrcl 7938 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 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-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-iota 5196 df-fun 5237 df-fv 5243 df-inn 8950 df-ndx 12515 df-slot 12516 |
This theorem is referenced by: imasbas 12784 imasplusg 12785 imasmulr 12786 |
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