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Mirrors > Home > ILE Home > Th. List > ndxarg | Unicode version |
Description: Get the numeric argument from a defined structure component extractor such as df-base 11563. (Contributed by Mario Carneiro, 6-Oct-2013.) |
Ref | Expression |
---|---|
ndxarg.1 |
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ndxarg.2 |
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Ref | Expression |
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ndxarg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ndx 11560 |
. . . 4
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2 | nnex 8491 |
. . . . 5
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3 | resiexg 4772 |
. . . . 5
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4 | 2, 3 | ax-mp 7 |
. . . 4
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5 | 1, 4 | eqeltri 2161 |
. . 3
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6 | ndxarg.1 |
. . 3
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7 | ndxarg.2 |
. . 3
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8 | 5, 6, 7 | strnfvn 11578 |
. 2
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9 | 1 | fveq1i 5321 |
. 2
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10 | fvresi 5506 |
. . 3
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11 | 7, 10 | ax-mp 7 |
. 2
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12 | 8, 9, 11 | 3eqtri 2113 |
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 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 3965 ax-pow 4017 ax-pr 4047 ax-un 4271 ax-cnex 7499 ax-resscn 7500 ax-1re 7502 ax-addrcl 7505 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 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-ral 2365 df-rex 2366 df-v 2624 df-sbc 2844 df-un 3006 df-in 3008 df-ss 3015 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-int 3697 df-br 3854 df-opab 3908 df-mpt 3909 df-id 4131 df-xp 4460 df-rel 4461 df-cnv 4462 df-co 4463 df-dm 4464 df-rn 4465 df-res 4466 df-iota 4995 df-fun 5032 df-fv 5038 df-inn 8486 df-ndx 11560 df-slot 11561 |
This theorem is referenced by: ndxid 11581 ndxslid 11582 strndxid 11585 basendx 11611 basendxnn 11612 plusgndx 11650 2strstrg 11657 2strbasg 11658 2stropg 11659 2strstr1g 11660 2strop1g 11662 basendxnplusgndx 11663 mulrndx 11667 basendxnmulrndx 11671 starvndx 11676 scandx 11684 vscandx 11687 ipndx 11695 tsetndx 11705 plendx 11712 |
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