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Mirrors > Home > ILE Home > Th. List > strslfv | Unicode version |
Description: Extract a structure
component ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
strfv.s |
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strslfv.e |
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strfv.n |
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Ref | Expression |
---|---|
strslfv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strslfv.e |
. 2
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2 | strfv.s |
. . 3
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3 | structex 11560 |
. . 3
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4 | 2, 3 | mp1i 10 |
. 2
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5 | 2 | structfun 11566 |
. . 3
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6 | 5 | a1i 9 |
. 2
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7 | strfv.n |
. . 3
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8 | 1 | simpri 112 |
. . . . 5
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9 | opexg 4064 |
. . . . 5
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10 | 8, 9 | mpan 416 |
. . . 4
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11 | snssg 3579 |
. . . 4
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12 | 10, 11 | syl 14 |
. . 3
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13 | 7, 12 | mpbiri 167 |
. 2
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14 | id 19 |
. 2
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15 | 1, 4, 6, 13, 14 | strslfv2d 11590 |
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-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-un 4269 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-ral 2365 df-rex 2366 df-rab 2369 df-v 2622 df-sbc 2842 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-nul 3288 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-mpt 3907 df-id 4129 df-xp 4457 df-rel 4458 df-cnv 4459 df-co 4460 df-dm 4461 df-rn 4462 df-res 4463 df-iota 4993 df-fun 5030 df-fv 5036 df-struct 11550 df-slot 11552 |
This theorem is referenced by: strslfv3 11593 |
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