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Theorem sbcreu 3344
 Description: Interchange class substitution and restricted uniqueness quantifier. (Contributed by NM, 24-Feb-2013.) (Revised by NM, 18-Aug-2018.)
Assertion
Ref Expression
sbcreu
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem sbcreu
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3277 . 2
2 reurex 3009 . . 3
3 sbcex 3277 . . . 4
43rexlimivw 2876 . . 3
52, 4syl 17 . 2
6 dfsbcq2 3270 . . 3
7 dfsbcq2 3270 . . . 4
87reubidv 2975 . . 3
9 nfcv 2592 . . . . 5
10 nfs1v 2266 . . . . 5
119, 10nfreu 2965 . . . 4
12 sbequ12 2083 . . . . 5
1312reubidv 2975 . . . 4
1411, 13sbie 2237 . . 3
156, 8, 14vtoclbg 3108 . 2
161, 5, 15pm5.21nii 355 1
 Colors of variables: wff setvar class Syntax hints:   wb 188   wceq 1444  wsb 1797   wcel 1887  wrex 2738  wreu 2739  cvv 3045  wsbc 3267 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-reu 2744  df-rmo 2745  df-v 3047  df-sbc 3268 This theorem is referenced by: (None)
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