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Theorem cbviota 5100
 Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.)
Hypotheses
Ref Expression
cbviota.1
cbviota.2
cbviota.3
Assertion
Ref Expression
cbviota

Proof of Theorem cbviota
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1509 . . . . . 6
2 nfs1v 1913 . . . . . . 7
3 nfv 1509 . . . . . . 7
42, 3nfbi 1569 . . . . . 6
5 sbequ12 1745 . . . . . . 7
6 equequ1 1689 . . . . . . 7
75, 6bibi12d 234 . . . . . 6
81, 4, 7cbval 1728 . . . . 5
9 cbviota.2 . . . . . . . 8
109nfsb 1920 . . . . . . 7
11 nfv 1509 . . . . . . 7
1210, 11nfbi 1569 . . . . . 6
13 nfv 1509 . . . . . 6
14 sbequ 1813 . . . . . . . 8
15 cbviota.3 . . . . . . . . 9
16 cbviota.1 . . . . . . . . 9
1715, 16sbie 1765 . . . . . . . 8
1814, 17syl6bb 195 . . . . . . 7
19 equequ1 1689 . . . . . . 7
2018, 19bibi12d 234 . . . . . 6
2112, 13, 20cbval 1728 . . . . 5
228, 21bitri 183 . . . 4
2322abbii 2256 . . 3
2423unieqi 3753 . 2
25 dfiota2 5096 . 2
26 dfiota2 5096 . 2
2724, 25, 263eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330   wceq 1332  wnf 1437  wsb 1736  cab 2126  cuni 3743  cio 5093 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-sn 3537  df-uni 3744  df-iota 5095 This theorem is referenced by:  cbviotav  5101  cbvriota  5747
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