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Theorem 3exbidv 1615
Description: Formula-building rule for 3 existential quantifiers (deduction rule). (Contributed by NM, 1-May-1995.)
Hypothesis
Ref Expression
3exbidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
3exbidv  |-  ( ph  ->  ( E. x E. y E. z ps  <->  E. x E. y E. z ch ) )
Distinct variable groups:    ph, x    ph, y    ph, z
Allowed substitution hints:    ps( x, y, z)    ch( x, y, z)

Proof of Theorem 3exbidv
StepHypRef Expression
1 3exbidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21exbidv 1612 . 2  |-  ( ph  ->  ( E. z ps  <->  E. z ch ) )
322exbidv 1614 1  |-  ( ph  ->  ( E. x E. y E. z ps  <->  E. x E. y E. z ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E.wex 1528
This theorem is referenced by:  ceqsex6v  2828  euotd  4267  oprabid  5882  eloprabga  5934  eloprabi  6186  bnj981  28982
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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