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Theorem sbcreu 3414
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:   ,   ,   ,

Proof of Theorem sbcreu
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3337 . 2
2 reurex 3074 . . 3
3 sbcex 3337 . . . 4
43rexlimivw 2946 . . 3
52, 4syl 16 . 2
6 dfsbcq2 3330 . . 3
7 dfsbcq2 3330 . . . 4
87reubidv 3042 . . 3
9 nfcv 2619 . . . . 5
10 nfs1v 2181 . . . . 5
119, 10nfreu 3032 . . . 4
12 sbequ12 1992 . . . . 5
1312reubidv 3042 . . . 4
1411, 13sbie 2149 . . 3
156, 8, 14vtoclbg 3168 . 2
161, 5, 15pm5.21nii 353 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  [wsb 1739  e.wcel 1818  E.wrex 2808  E!wreu 2809   cvv 3109  [.wsbc 3327
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111  df-sbc 3328
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