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Theorem 19.41vvvv 1841
Description: Version of 19.41 2070 with four quantifiers and a dv condition requiring fewer axioms. (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 1840 . . 3  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
21exbii 1726 . 2  |-  ( E. w E. x E. y E. z ( ph  /\ 
ps )  <->  E. w
( E. x E. y E. z ph  /\  ps ) )
3 19.41v 1838 . 2  |-  ( E. w ( E. x E. y E. z ph  /\ 
ps )  <->  ( E. w E. x E. y E. z ph  /\  ps ) )
42, 3bitri 257 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 setvar class
Syntax hints:    <-> wb 189    /\ wa 376   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by:  elfuns  30753
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