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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 12518. (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 12515 |
. . . 4
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2 | nnex 8955 |
. . . . 5
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3 | resiexg 4970 |
. . . . 5
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4 | 2, 3 | ax-mp 5 |
. . . 4
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5 | 1, 4 | eqeltri 2262 |
. . 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 12533 |
. 2
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9 | 1 | fveq1i 5535 |
. 2
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10 | fvresi 5730 |
. . 3
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11 | 7, 10 | ax-mp 5 |
. 2
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12 | 8, 9, 11 | 3eqtri 2214 |
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: ndxid 12536 ndxslid 12537 strndxid 12540 basendx 12567 basendxnn 12568 plusgndx 12621 2strstrg 12630 2strbasg 12631 2stropg 12632 2strstr1g 12633 2strop1g 12635 basendxnplusgndx 12636 mulrndx 12641 basendxnmulrndx 12645 starvndx 12650 scandx 12662 vscandx 12668 ipndx 12680 tsetndx 12697 plendx 12711 dsndx 12722 unifndx 12733 |
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