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Theorem 19.41vvvv 1898
Description: Theorem 19.41 of [Margaris] p. 90 with 4 quantifiers. (Contributed by FL, 14-Jul-2007.)
Assertion
Ref Expression
19.41vvvv  |-  ( E. w E. x E. y E. z ( ph  /\ 
ps )  <->  ( E. w E. x E. y E. z ph  /\  ps ) )
Distinct variable groups:    ps, w    ps, x    ps, y    ps, z
Allowed substitution hints:    ph( x, y, z, w)

Proof of Theorem 19.41vvvv
StepHypRef Expression
1 19.41vvv 1897 . . 3  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
21exbii 1598 . 2  |-  ( E. w E. x E. y E. z ( ph  /\ 
ps )  <->  E. w
( E. x E. y E. z ph  /\  ps ) )
3 19.41v 1895 . 2  |-  ( E. w ( E. x E. y E. z ph  /\ 
ps )  <->  ( E. w E. x E. y E. z ph  /\  ps ) )
42, 3bitri 183 1  |-  ( E. w E. x E. y E. z ( ph  /\ 
ps )  <->  ( E. w E. x E. y E. z ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E.wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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