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Theorem cbvreu 2930
 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 1629 . . . 4
21sb8eu 2299 . . 3
3 sban 2139 . . . 4
43eubii 2290 . . 3
5 clelsb3 2538 . . . . . 6
65anbi1i 677 . . . . 5
76eubii 2290 . . . 4
8 nfv 1629 . . . . . 6
9 cbvral.1 . . . . . . 7
109nfsb 2185 . . . . . 6
118, 10nfan 1846 . . . . 5
12 nfv 1629 . . . . 5
13 eleq1 2496 . . . . . 6
14 sbequ 2111 . . . . . . 7
15 cbvral.2 . . . . . . . 8
16 cbvral.3 . . . . . . . 8
1715, 16sbie 2149 . . . . . . 7
1814, 17syl6bb 253 . . . . . 6
1913, 18anbi12d 692 . . . . 5
2011, 12, 19cbveu 2301 . . . 4
217, 20bitri 241 . . 3
222, 4, 213bitri 263 . 2
23 df-reu 2712 . 2
24 df-reu 2712 . 2
2522, 23, 243bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553  wsb 1658   wcel 1725  weu 2281  wreu 2707 This theorem is referenced by:  cbvrmo  2931  cbvreuv  2934  cbvriota  6560 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-cleq 2429  df-clel 2432  df-reu 2712
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