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Theorem disjxwwlks 24440
 Description: Sets of walks (as words) extended by an edge are disjunct if each set contains extensions of distinct walks. (Contributed by Alexander van der Vekens, 29-Jul-2018.)
Assertion
Ref Expression
disjxwwlks Disj WWalksN Word substr lastS lastS
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem disjxwwlks
StepHypRef Expression
1 simp1 996 . . . . 5 substr lastS lastS substr
21a1i 11 . . . 4 Word substr lastS lastS substr
32ss2rabi 3582 . . 3 Word substr lastS lastS Word substr
43rgenw 2825 . 2 WWalksN Word substr lastS lastS Word substr
5 disjxwrd 12643 . 2 Disj WWalksN Word substr
6 disjss2 4420 . 2 WWalksN Word substr lastS lastS Word substr Disj WWalksN Word substr Disj WWalksN Word substr lastS lastS
74, 5, 6mp2 9 1 Disj WWalksN Word substr lastS lastS
 Colors of variables: wff setvar class Syntax hints:   wi 4   w3a 973   wceq 1379   wcel 1767  wral 2814  crab 2818   wss 3476  cpr 4029  cop 4033  Disj wdisj 4417   crn 5000  cfv 5588  (class class class)co 6284  cc0 9492  Word cword 12500   lastS clsw 12501   substr csubstr 12504   WWalksN cwwlkn 24382 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rmo 2822  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-disj 4418  df-br 4448  df-iota 5551  df-fv 5596  df-ov 6287 This theorem is referenced by: (None)
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