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Theorem rexsn 3874
 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 3871 . 2
41, 3ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   wcel 1727  wrex 2712  cvv 2962  csn 3838 This theorem is referenced by:  elsnres  5211  oarec  6834  snec  6996  zornn0g  8416  fpwwe2lem13  8548  elreal  9037  vdwlem6  13385  restsn  17265  snclseqg  18176  ust0  18280  eldm3  25416  heiborlem3  26560 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-rex 2717  df-v 2964  df-sbc 3168  df-sn 3844
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