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Theorem 2ralunsn 3598
 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:   ,   ,,   ,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()   ()   ()

Proof of Theorem 2ralunsn
StepHypRef Expression
1 2ralunsn.2 . . . 4
21ralunsn 3597 . . 3
32ralbidv 2369 . 2
4 2ralunsn.1 . . . . . 6
54ralbidv 2369 . . . . 5
6 2ralunsn.3 . . . . 5
75, 6anbi12d 457 . . . 4
87ralunsn 3597 . . 3
9 r19.26 2486 . . . 4
109anbi1i 446 . . 3
118, 10syl6bb 194 . 2
123, 11bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  wral 2349   cun 2972  csn 3406 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-v 2604  df-sbc 2817  df-un 2978  df-sn 3412 This theorem is referenced by: (None)
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