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Theorem 3exbii 1816
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 1814 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1815 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  4exdistr  1927  ceqsex6v  3279  oprabid  6717  dfoprab2  6743  dftpos3  7415  xpassen  8095  bnj916  31129  bnj917  31130  bnj983  31147  bnj996  31151  bnj1021  31160  bnj1033  31163  ellines  32384  rnxrn  34296
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