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Theorem 3exbii 1674
Description: Inference adding 3 existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)
Hypothesis
Ref Expression
3exbii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
3exbii  |-  ( E. x E. y E. z ph  <->  E. x E. y E. z ps )

Proof of Theorem 3exbii
StepHypRef Expression
1 3exbii.1 . . 3  |-  ( ph  <->  ps )
21exbii 1672 . 2  |-  ( E. z ph  <->  E. z ps )
322exbii 1673 1  |-  ( E. x E. y E. z ph  <->  E. x E. y E. z ps )
Colors of variables: wff setvar class
Syntax hints:    <-> 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
This theorem depends on definitions:  df-bi 185  df-ex 1618
This theorem is referenced by:  4exdistr  1786  ceqsex6v  3148  oprabid  6297  dfoprab2  6316  dftpos3  6965  xpassen  7604  ellines  30030  bnj916  34392  bnj917  34393  bnj983  34410  bnj996  34414  bnj1021  34423  bnj1033  34426
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