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Theorem 4exbidv 1723
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 1721 . 2  |-  ( ph  ->  ( E. z E. w ps  <->  E. z E. w ch ) )
322exbidv 1721 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 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  ceqsex8v  3149  copsex4g  4725  opbrop  5068  ov3  6412  brecop  7396  addsrmo  9439  mulsrmo  9440  addsrpr  9441  mulsrpr  9442  dihopelvalcpre  37372  xihopellsmN  37378  dihopellsm  37379
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