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Mirrors > Home > ILE Home > Th. List > plendxnn | Unicode version |
Description: The index value of the order slot is a positive integer. This property should be ensured for every concrete coding because otherwise it could not be used in an extensible structure (slots must be positive integers). (Contributed by AV, 30-Oct-2024.) |
Ref | Expression |
---|---|
plendxnn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | plendx 12807 |
. 2
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2 | 10nn 9453 |
. 2
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3 | 1, 2 | eqeltri 2266 |
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 2166 ax-14 2167 ax-ext 2175 ax-sep 4147 ax-pow 4203 ax-pr 4238 ax-un 4462 ax-cnex 7953 ax-resscn 7954 ax-1cn 7955 ax-1re 7956 ax-icn 7957 ax-addcl 7958 ax-addrcl 7959 ax-mulcl 7960 ax-mulcom 7963 ax-addass 7964 ax-mulass 7965 ax-distr 7966 ax-1rid 7969 ax-0id 7970 ax-cnre 7973 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2045 df-mo 2046 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-rab 2481 df-v 2762 df-sbc 2986 df-un 3157 df-in 3159 df-ss 3166 df-pw 3603 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-int 3871 df-br 4030 df-opab 4091 df-mpt 4092 df-id 4322 df-xp 4661 df-rel 4662 df-cnv 4663 df-co 4664 df-dm 4665 df-rn 4666 df-res 4667 df-iota 5207 df-fun 5248 df-fv 5254 df-ov 5913 df-inn 8973 df-2 9031 df-3 9032 df-4 9033 df-5 9034 df-6 9035 df-7 9036 df-8 9037 df-9 9038 df-dec 9439 df-ndx 12611 df-slot 12612 df-ple 12705 |
This theorem is referenced by: prdsex 12870 znval 14101 znbaslemnn 14104 |
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