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Theorem 3exbii 1925
Description: Inference adding three existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)
Hypothesis
Ref Expression
3exbii.1 (𝜑𝜓)
Assertion
Ref Expression
3exbii (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)

Proof of Theorem 3exbii
StepHypRef Expression
1 3exbii.1 . . 3 (𝜑𝜓)
21exbii 1923 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1924 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  4exdistr  2038  ceqsex6v  3397  oprabid  6821  dfoprab2  6847  dftpos3  7521  xpassen  8209  bnj916  31335  bnj917  31336  bnj983  31353  bnj996  31357  bnj1021  31366  bnj1033  31369  ellines  32590  rnxrn  34491
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