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Theorem 4exbidv 1616
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 1614 . 2  |-  ( ph  ->  ( E. z E. w ps  <->  E. z E. w ch ) )
322exbidv 1614 1  |-  ( ph  ->  ( E. x E. y E. z E. w ps 
<->  E. x E. y E. z E. w ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E.wex 1528
This theorem is referenced by:  ceqsex8v  2829  copsex4g  4255  opbrop  4767  ov3  5984  brecop  6751  th3q  6767  elo  25041  eloi  25086  dihopelvalcpre  31438  xihopellsmN  31444  dihopellsm  31445
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603
This theorem depends on definitions:  df-bi 177  df-ex 1529
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