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Theorem 19.41vvv 1846
Description: Theorem 19.41 of [Margaris] p. 90 with 3 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vvv  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
Distinct variable groups:    ps, x    ps, y    ps, z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem 19.41vvv
StepHypRef Expression
1 19.41vv 1845 . . 3  |-  ( E. y E. z (
ph  /\  ps )  <->  ( E. y E. z ph  /\  ps ) )
21exbii 1571 . 2  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( E. y E. z ph  /\ 
ps ) )
3 19.41v 1844 . 2  |-  ( E. x ( E. y E. z ph  /\  ps ) 
<->  ( E. x E. y E. z ph  /\  ps ) )
42, 3bitri 240 1  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1530
This theorem is referenced by:  19.41vvvv  1847  eloprabga  5936  dftpos3  6254  eeeeanv  24955
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-nf 1534
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