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Theorem 4exbidv 1685
Description: Formula-building rule for 4 existential quantifiers (deduction rule). (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
4exbidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
4exbidv  |-  ( ph  ->  ( E. x E. y E. z E. w ps 
<->  E. x E. y E. z E. w ch ) )
Distinct variable groups:    ph, x    ph, y    ph, z    ph, w
Allowed substitution hints:    ps( x, y, z, w)    ch( x, y, z, w)

Proof of Theorem 4exbidv
StepHypRef Expression
1 4exbidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
212exbidv 1683 . 2  |-  ( ph  ->  ( E. z E. w ps  <->  E. z E. w ch ) )
322exbidv 1683 1  |-  ( ph  ->  ( E. x E. y E. z E. w ps 
<->  E. x E. y E. z E. w ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  ceqsex8v  3111  copsex4g  4678  opbrop  5014  ov3  6327  brecop  7293  th3q  7309  dihopelvalcpre  35199  xihopellsmN  35205  dihopellsm  35206
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