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Theorem 3exbii 1641
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 1639 . 2  |-  ( E. z ph  <->  E. z ps )
322exbii 1640 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 1591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607
This theorem depends on definitions:  df-bi 185  df-ex 1592
This theorem is referenced by:  4exdistr  1948  ceqsex6v  3148  oprabid  6299  dfoprab2  6318  dftpos3  6963  xpassen  7601  ellines  29365  bnj916  32945  bnj917  32946  bnj983  32963  bnj996  32967  bnj1021  32976  bnj1033  32979
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