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Theorem cbvriota 5787
 Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
cbvriota.1
cbvriota.2
cbvriota.3
Assertion
Ref Expression
cbvriota
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvriota
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2220 . . . . 5
2 sbequ12 1751 . . . . 5
31, 2anbi12d 465 . . . 4
4 nfv 1508 . . . 4
5 nfv 1508 . . . . 5
6 nfs1v 1919 . . . . 5
75, 6nfan 1545 . . . 4
83, 4, 7cbviota 5139 . . 3
9 eleq1 2220 . . . . 5
10 sbequ 1820 . . . . . 6
11 cbvriota.2 . . . . . . 7
12 cbvriota.3 . . . . . . 7
1311, 12sbie 1771 . . . . . 6
1410, 13bitrdi 195 . . . . 5
159, 14anbi12d 465 . . . 4
16 nfv 1508 . . . . 5
17 cbvriota.1 . . . . . 6
1817nfsb 1926 . . . . 5
1916, 18nfan 1545 . . . 4
20 nfv 1508 . . . 4
2115, 19, 20cbviota 5139 . . 3
228, 21eqtri 2178 . 2
23 df-riota 5777 . 2
24 df-riota 5777 . 2
2522, 23, 243eqtr4i 2188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335  wnf 1440  wsb 1742   wcel 2128  cio 5132  crio 5776 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-sn 3566  df-uni 3773  df-iota 5134  df-riota 5777 This theorem is referenced by:  cbvriotav  5788
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