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Theorem cbviota 5561
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 1707 . . . . . 6
2 nfs1v 2181 . . . . . . 7
3 nfv 1707 . . . . . . 7
42, 3nfbi 1934 . . . . . 6
5 sbequ12 1992 . . . . . . 7
6 equequ1 1798 . . . . . . 7
75, 6bibi12d 321 . . . . . 6
81, 4, 7cbval 2021 . . . . 5
9 cbviota.2 . . . . . . . 8
109nfsb 2184 . . . . . . 7
11 nfv 1707 . . . . . . 7
1210, 11nfbi 1934 . . . . . 6
13 nfv 1707 . . . . . 6
14 sbequ 2117 . . . . . . . 8
15 cbviota.3 . . . . . . . . 9
16 cbviota.1 . . . . . . . . 9
1715, 16sbie 2149 . . . . . . . 8
1814, 17syl6bb 261 . . . . . . 7
19 equequ1 1798 . . . . . . 7
2018, 19bibi12d 321 . . . . . 6
2112, 13, 20cbval 2021 . . . . 5
228, 21bitri 249 . . . 4
2322abbii 2591 . . 3
2423unieqi 4258 . 2
25 dfiota2 5557 . 2
26 dfiota2 5557 . 2
2724, 25, 263eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  [wsb 1739  {cab 2442  U.cuni 4249  iotacio 5554
This theorem is referenced by:  cbviotav  5562  fvopab5  5979  cbvriota  6267
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-sn 4030  df-uni 4250  df-iota 5556
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