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Theorem cbviota 5554
 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 1763 . . . . . 6
2 nfs1v 2268 . . . . . . 7
3 nfv 1763 . . . . . . 7
42, 3nfbi 2019 . . . . . 6
5 sbequ12 2085 . . . . . . 7
6 equequ1 1869 . . . . . . 7
75, 6bibi12d 323 . . . . . 6
81, 4, 7cbval 2116 . . . . 5
9 cbviota.2 . . . . . . . 8
109nfsb 2271 . . . . . . 7
11 nfv 1763 . . . . . . 7
1210, 11nfbi 2019 . . . . . 6
13 nfv 1763 . . . . . 6
14 sbequ 2207 . . . . . . . 8
15 cbviota.3 . . . . . . . . 9
16 cbviota.1 . . . . . . . . 9
1715, 16sbie 2239 . . . . . . . 8
1814, 17syl6bb 265 . . . . . . 7
19 equequ1 1869 . . . . . . 7
2018, 19bibi12d 323 . . . . . 6
2112, 13, 20cbval 2116 . . . . 5
228, 21bitri 253 . . . 4
2322abbii 2569 . . 3
2423unieqi 4210 . 2
25 dfiota2 5550 . 2
26 dfiota2 5550 . 2
2724, 25, 263eqtr4i 2485 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1444   wceq 1446  wnf 1669  wsb 1799  cab 2439  cuni 4201  cio 5547 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-rex 2745  df-sn 3971  df-uni 4202  df-iota 5549 This theorem is referenced by:  cbviotav  5555  fvopab5  5979  cbvriota  6267
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