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Theorem ralsn 3767
 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 3765 . 2
41, 3ax-mp 8 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642   wcel 1710  wral 2614  cvv 2859  csn 3737 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-sbc 3047  df-sn 3741 This theorem is referenced by: (None)
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