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Theorem cbvriota 5506
 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 2116 . . . . 5
2 sbequ12 1670 . . . . 5
31, 2anbi12d 450 . . . 4
4 nfv 1437 . . . 4
5 nfv 1437 . . . . 5
6 nfs1v 1831 . . . . 5
75, 6nfan 1473 . . . 4
83, 4, 7cbviota 4900 . . 3
9 eleq1 2116 . . . . 5
10 sbequ 1737 . . . . . 6
11 cbvriota.2 . . . . . . 7
12 cbvriota.3 . . . . . . 7
1311, 12sbie 1690 . . . . . 6
1410, 13syl6bb 189 . . . . 5
159, 14anbi12d 450 . . . 4
16 nfv 1437 . . . . 5
17 cbvriota.1 . . . . . 6
1817nfsb 1838 . . . . 5
1916, 18nfan 1473 . . . 4
20 nfv 1437 . . . 4
2115, 19, 20cbviota 4900 . . 3
228, 21eqtri 2076 . 2
23 df-riota 5496 . 2
24 df-riota 5496 . 2
2522, 23, 243eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wceq 1259  wnf 1365   wcel 1409  wsb 1661  cio 4893  crio 5495 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-sn 3409  df-uni 3609  df-iota 4895  df-riota 5496 This theorem is referenced by:  cbvriotav  5507
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