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Theorem exlimivv 1776
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 1-Aug-1995.)
Hypothesis
Ref Expression
exlimivv.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
exlimivv  |-  ( E. x E. y ph  ->  ps )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem exlimivv
StepHypRef Expression
1 exlimivv.1 . . 3  |-  ( ph  ->  ps )
21exlimiv 1489 . 2  |-  ( E. y ph  ->  ps )
32exlimiv 1489 1  |-  ( E. x E. y ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1338  ax-ie2 1383  ax-17 1419
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  cgsex2g  2590  cgsex4g  2591  opabss  3821  copsexg  3981  elopab  3995  epelg  4027  0nelelxp  4373  elvvuni  4404  optocl  4416  xpsspw  4450  relopabi  4463  relop  4486  elreldm  4560  xpmlem  4744  dfco2a  4821  unielrel  4845  oprabid  5537  1stval2  5782  2ndval2  5783  xp1st  5792  xp2nd  5793  poxp  5853  rntpos  5872  dftpos4  5878  tpostpos  5879  tfrlem7  5933  th3qlem2  6209  ener  6259  domtr  6265  unen  6293  xpsnen  6295  ltdcnq  6493  archnqq  6513  enq0tr  6530  nqnq0pi  6534  nqnq0  6537  nqpnq0nq  6549  nqnq0a  6550  nqnq0m  6551  nq0m0r  6552  nq0a0  6553  nq02m  6561  prarloc  6599  axaddcl  6938  axmulcl  6940  bj-inex  10000
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