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Theorem 3exbii 1600
Description: Inference adding 3 existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)
Hypothesis
Ref Expression
exbii.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 exbii.1 . . 3  |-  ( ph  <->  ps )
21exbii 1598 . 2  |-  ( E. z ph  <->  E. z ps )
322exbii 1599 1  |-  ( E. x E. y E. z ph  <->  E. x E. y E. z ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   E.wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eeeanv  1926  ceqsex6v  2774  oprabid  5882  dfoprab2  5897  dftpos3  6238  xpassen  6804
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