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Theorem cbvreu 2525
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  F/
cbvral.2  F/
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 1418 . . . 4  F/
21sb8eu 1910 . . 3
3 sban 1826 . . . 4
43eubii 1906 . . 3
5 clelsb3 2139 . . . . . 6
65anbi1i 431 . . . . 5
76eubii 1906 . . . 4
8 nfv 1418 . . . . . 6  F/
9 cbvral.1 . . . . . . 7  F/
109nfsb 1819 . . . . . 6  F/
118, 10nfan 1454 . . . . 5  F/
12 nfv 1418 . . . . 5  F/
13 eleq1 2097 . . . . . 6
14 sbequ 1718 . . . . . . 7
15 cbvral.2 . . . . . . . 8  F/
16 cbvral.3 . . . . . . . 8
1715, 16sbie 1671 . . . . . . 7
1814, 17syl6bb 185 . . . . . 6
1913, 18anbi12d 442 . . . . 5
2011, 12, 19cbveu 1921 . . . 4
217, 20bitri 173 . . 3
222, 4, 213bitri 195 . 2
23 df-reu 2307 . 2
24 df-reu 2307 . 2
2522, 23, 243bitr4i 201 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   F/wnf 1346   wcel 1390  wsb 1642  weu 1897  wreu 2302
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-cleq 2030  df-clel 2033  df-reu 2307
This theorem is referenced by:  cbvrmo  2526  cbvreuv  2529
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