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Theorem 19.41vv 1946
Description: Theorem 19.41 of [Margaris] p. 90 with 2 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vv  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.41vv
StepHypRef Expression
1 19.41v 1945 . . 3  |-  ( E. y ( ph  /\  ps )  <->  ( E. y ph  /\  ps ) )
21exbii 1644 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( E. y ph  /\  ps ) )
3 19.41v 1945 . 2  |-  ( E. x ( E. y ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
42, 3bitri 249 1  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x E. y ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600
This theorem is referenced by:  19.41vvv  1947  rabxp  5035  copsex2gb  5111  mpt2mptx  6375  xpassen  7608  dfac5lem1  8500  3v3e3cycl  24341  dfdm5  28783  dfrn5  28784  elima4  28786  brtxp2  29108  brpprod3a  29113  brimg  29164  brsuccf  29168  mpt2mptx2  31988  bnj996  33092  diblsmopel  35968
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