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Theorem ralsn 4068
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:   ,   ,

Proof of Theorem ralsn
StepHypRef Expression
1 ralsn.1 . 2
2 ralsn.2 . . 3
32ralsng 4064 . 2
41, 3ax-mp 5 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  A.wral 2807   cvv 3109  {csn 4029
This theorem is referenced by:  elixpsn  7528  frfi  7785  dffi3  7911  fseqenlem1  8426  fpwwe2lem13  9041  hashbc  12502  hashf1lem1  12504  cshw1  12790  rpnnen2lem11  13958  drsdirfi  15567  0subg  16226  efgsp1  16755  dprd2da  17091  lbsextlem4  17807  ply1coe  18337  mat0dimcrng  18972  txkgen  20153  xkoinjcn  20188  isufil2  20409  ust0  20722  prdsxmetlem  20871  prdsbl  20994  finiunmbl  21954  xrlimcnp  23298  chtub  23487  2sqlem10  23649  dchrisum0flb  23695  pntpbnd1  23771  usgra1v  24390  constr1trl  24590  clwwlkel  24793  rusgranumwlkl1  24947  h1deoi  26467  subfacp1lem5  28628  cvmlift2lem1  28747  cvmlift2lem12  28759  heibor1lem  30305  bnj149  33933
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-v 3111  df-sbc 3328  df-sn 4030
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