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Theorem cshwsexa 12792
Description: The class of (different!) words resulting by cyclically shifting something (not necessarily a word) is a set. (Contributed by AV, 8-Jun-2018.) (Revised by Mario Carneiro/AV, 25-Oct-2018.)
Assertion
Ref Expression
cshwsexa
Distinct variable groups:   ,   , ,

Proof of Theorem cshwsexa
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-rab 2816 . . 3
2 r19.42v 3012 . . . . 5
32bicomi 202 . . . 4
43abbii 2591 . . 3
5 df-rex 2813 . . . 4
65abbii 2591 . . 3
71, 4, 63eqtri 2490 . 2
8 abid2 2597 . . . 4
9 ovex 6324 . . . 4
108, 9eqeltri 2541 . . 3
11 tru 1399 . . . . 5
1211, 11pm3.2i 455 . . . 4
13 ovex 6324 . . . . . . 7
1413a1i 11 . . . . . 6
15 eqtr3 2485 . . . . . . . . . . . . 13
1615ex 434 . . . . . . . . . . . 12
1716eqcoms 2469 . . . . . . . . . . 11
1817adantl 466 . . . . . . . . . 10
1918com12 31 . . . . . . . . 9
2019ad2antlr 726 . . . . . . . 8
2120alrimiv 1719 . . . . . . 7
2221ex 434 . . . . . 6
2314, 22spcimedv 3193 . . . . 5
2423imp 429 . . . 4
2512, 24mp1i 12 . . 3
2610, 25zfrep4 4571 . 2
277, 26eqeltri 2541 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395   wtru 1396  E.wex 1612  e.wcel 1818  {cab 2442  E.wrex 2808  {crab 2811   cvv 3109  `cfv 5593  (class class class)co 6296  0cc0 9513   cfzo 11824   chash 12405  Wordcword 12534   ccsh 12759
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-rep 4563  ax-nul 4581
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-fv 5601  df-ov 6299
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