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Theorem 2ralunsn 3832
 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 3831 . . 3
32ralbidv 2576 . 2
4 2ralunsn.1 . . . . . 6
54ralbidv 2576 . . . . 5
6 2ralunsn.3 . . . . 5
75, 6anbi12d 691 . . . 4
87ralunsn 3831 . . 3
9 r19.26 2688 . . . 4
109anbi1i 676 . . 3
118, 10syl6bb 252 . 2
123, 11bitrd 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696  wral 2556   cun 3163  csn 3653 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-v 2803  df-sbc 3005  df-un 3170  df-sn 3659
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