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Theorem ralunsn 3760
 Description: Restricted quantification over the union of a set and a singleton, using implicit substitution. (Contributed by Paul Chapman, 17-Nov-2012.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
ralunsn.1
Assertion
Ref Expression
ralunsn
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ralunsn
StepHypRef Expression
1 ralunb 3288 . 2
2 ralunsn.1 . . . 4
32ralsng 3599 . . 3
43anbi2d 460 . 2
51, 4syl5bb 191 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1335   wcel 2128  wral 2435   cun 3100  csn 3560 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-v 2714  df-sbc 2938  df-un 3106  df-sn 3566 This theorem is referenced by:  2ralunsn  3761
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