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Theorem 3exbii 1723
Description: Inference adding three 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 1721 . 2  |-  ( E. z ph  <->  E. z ps )
322exbii 1722 1  |-  ( E. x E. y E. z ph  <->  E. x E. y E. z ps )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189   E.wex 1666
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1672  ax-4 1685
This theorem depends on definitions:  df-bi 190  df-ex 1667
This theorem is referenced by:  4exdistr  1843  ceqsex6v  3057  oprabid  6302  dfoprab2  6324  dftpos3  6977  xpassen  7652  bnj916  29749  bnj917  29750  bnj983  29767  bnj996  29771  bnj1021  29780  bnj1033  29783  ellines  30924
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