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Theorem 2ralunsn 4238
 Description: Double restricted quantification over the union of a set and a singleton, using implicit substitution. (Contributed by Paul Chapman, 17-Nov-2012.)
Hypotheses
Ref Expression
2ralunsn.1
2ralunsn.2
2ralunsn.3
Assertion
Ref Expression
2ralunsn
Distinct variable groups:   ,   ,,   ,   ,   ,   ,

Proof of Theorem 2ralunsn
StepHypRef Expression
1 2ralunsn.2 . . . 4
21ralunsn 4237 . . 3
32ralbidv 2896 . 2
4 2ralunsn.1 . . . . . 6
54ralbidv 2896 . . . . 5
6 2ralunsn.3 . . . . 5
75, 6anbi12d 710 . . . 4
87ralunsn 4237 . . 3
9 r19.26 2984 . . . 4
109anbi1i 695 . . 3
118, 10syl6bb 261 . 2
123, 11bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  u.cun 3473  {csn 4029 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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030
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