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Theorem ralsng 3452
 Description: Substitution expressed in terms of quantification over a singleton. (Contributed by NM, 14-Dec-2005.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypothesis
Ref Expression
ralsng.1
Assertion
Ref Expression
ralsng
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ralsng
StepHypRef Expression
1 ralsns 3450 . 2
2 ralsng.1 . . 3
32sbcieg 2856 . 2
41, 3bitrd 186 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wral 2353  wsbc 2825  csn 3417 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 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-v 2612  df-sbc 2826  df-sn 3423 This theorem is referenced by:  ralsn  3455  ralprg  3462  raltpg  3464  ralunsn  3610  iinxsng  3772  posng  4459  fimaxre2  10294
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