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Theorem cbvreu 2833
 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 1619 . . . 4
21sb8eu 2222 . . 3
3 sban 2069 . . . 4
43eubii 2213 . . 3
5 clelsb3 2455 . . . . . 6
65anbi1i 676 . . . . 5
76eubii 2213 . . . 4
8 nfv 1619 . . . . . 6
9 cbvral.1 . . . . . . 7
109nfsb 2109 . . . . . 6
118, 10nfan 1824 . . . . 5
12 nfv 1619 . . . . 5
13 eleq1 2413 . . . . . 6
14 sbequ 2060 . . . . . . 7
15 cbvral.2 . . . . . . . 8
16 cbvral.3 . . . . . . . 8
1715, 16sbie 2038 . . . . . . 7
1814, 17syl6bb 252 . . . . . 6
1913, 18anbi12d 691 . . . . 5
2011, 12, 19cbveu 2224 . . . 4
217, 20bitri 240 . . 3
222, 4, 213bitri 262 . 2
23 df-reu 2621 . 2
24 df-reu 2621 . 2
2522, 23, 243bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wceq 1642  wsb 1648   wcel 1710  weu 2204  wreu 2616 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-cleq 2346  df-clel 2349  df-reu 2621 This theorem is referenced by:  cbvrmo  2834  cbvreuv  2837
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