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Theorem cbvreu 3086
 Description: Change the bound variable of a restricted uniqueness quantifier using implicit substitution. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
cbvral.1
cbvral.2
cbvral.3
Assertion
Ref Expression
cbvreu
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvreu
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1683 . . . 4
21sb8eu 2314 . . 3
3 sban 2114 . . . 4
43eubii 2300 . . 3
5 clelsb3 2588 . . . . . 6
65anbi1i 695 . . . . 5
76eubii 2300 . . . 4
8 nfv 1683 . . . . . 6
9 cbvral.1 . . . . . . 7
109nfsb 2168 . . . . . 6
118, 10nfan 1875 . . . . 5
12 nfv 1683 . . . . 5
13 eleq1 2539 . . . . . 6
14 sbequ 2090 . . . . . . 7
15 cbvral.2 . . . . . . . 8
16 cbvral.3 . . . . . . . 8
1715, 16sbie 2123 . . . . . . 7
1814, 17syl6bb 261 . . . . . 6
1913, 18anbi12d 710 . . . . 5
2011, 12, 19cbveu 2318 . . . 4
217, 20bitri 249 . . 3
222, 4, 213bitri 271 . 2
23 df-reu 2821 . 2
24 df-reu 2821 . 2
2522, 23, 243bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wnf 1599  wsb 1711   wcel 1767  weu 2275  wreu 2816 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-cleq 2459  df-clel 2462  df-reu 2821 This theorem is referenced by:  cbvrmo  3087  cbvreuv  3090  fourierdlem50  31473
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