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Theorem rexsn 3768
 Description: Restricted existential quantification over a singleton. (Contributed by Jeff Madsen, 5-Jan-2011.)
Hypotheses
Ref Expression
ralsn.1
ralsn.2
Assertion
Ref Expression
rexsn
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rexsn
StepHypRef Expression
1 ralsn.1 . 2
2 ralsn.2 . . 3
32rexsng 3766 . 2
41, 3ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642   wcel 1710  wrex 2615  cvv 2859  csn 3737 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-rex 2620  df-v 2861  df-sbc 3047  df-sn 3741 This theorem is referenced by:  pw1sn  4165  elimaksn  4283  setswith  4321  addcid1  4405  ltfintrilem1  4465  nnadjoin  4520  tfinnn  4534  elsnres  4996  xpnedisj  5513  snec  5987  lec0cg  6198  addccan2nclem1  6263
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