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Theorem 4exbidv 1620
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 1618 . 2  |-  ( ph  ->  ( E. z E. w ps  <->  E. z E. w ch ) )
322exbidv 1618 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 1531
This theorem is referenced by:  ceqsex8v  2842  copsex4g  4271  opbrop  4783  ov3  6000  brecop  6767  th3q  6783  elo  25144  eloi  25189  dihopelvalcpre  32060  xihopellsmN  32066  dihopellsm  32067
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606
This theorem depends on definitions:  df-bi 177  df-ex 1532
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