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Mirrors > Home > MPE Home > Th. List > iswwlkn | Structured version Visualization version Unicode version |
Description: Properties of a word to represent a walk of a fixed length (in an undirected graph). (Contributed by Alexander van der Vekens, 15-Jul-2018.) |
Ref | Expression |
---|---|
iswwlkn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wwlkn 25410 |
. . 3
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2 | 1 | eleq2d 2514 |
. 2
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3 | fveq2 5865 |
. . . 4
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4 | 3 | eqeq1d 2453 |
. . 3
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5 | 4 | elrab 3196 |
. 2
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6 | 2, 5 | syl6bb 265 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 ax-cnex 9595 ax-resscn 9596 ax-1cn 9597 ax-icn 9598 ax-addcl 9599 ax-addrcl 9600 ax-mulcl 9601 ax-mulrcl 9602 ax-i2m1 9607 ax-1ne0 9608 ax-rrecex 9611 ax-cnre 9612 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 986 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-pss 3420 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-tp 3973 df-op 3975 df-uni 4199 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-tr 4498 df-eprel 4745 df-id 4749 df-po 4755 df-so 4756 df-fr 4793 df-we 4795 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-pred 5380 df-ord 5426 df-on 5427 df-lim 5428 df-suc 5429 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-om 6693 df-wrecs 7028 df-recs 7090 df-rdg 7128 df-nn 10610 df-n0 10870 df-wwlkn 25408 |
This theorem is referenced by: wwlknimp 25415 wwlkn0 25417 wlklniswwlkn1 25427 wlklniswwlkn2 25428 wwlkiswwlkn 25430 vfwlkniswwlkn 25434 wwlknred 25451 wwlknext 25452 wwlkextproplem3 25471 clwwlkel 25521 clwwlkf 25522 wwlksubclwwlk 25532 rusgranumwlkl1 25675 rusgra0edg 25683 |
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