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Theorem ralsn 3444
 Description: Convert a quantification over a singleton to a substitution. (Contributed by NM, 27-Apr-2009.)
Hypotheses
Ref Expression
ralsn.1
ralsn.2
Assertion
Ref Expression
ralsn
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ralsn
StepHypRef Expression
1 ralsn.1 . 2
2 ralsn.2 . . 3
32ralsng 3441 . 2
41, 3ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285   wcel 1434  wral 2349  cvv 2602  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-sn 3412 This theorem is referenced by:  tfr0dm  5971
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