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Theorem 3exbii 1774
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 1772 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1773 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-ex 1702
This theorem is referenced by:  4exdistr  1926  ceqsex6v  3239  oprabid  6632  dfoprab2  6655  dftpos3  7316  xpassen  7999  bnj916  30703  bnj917  30704  bnj983  30721  bnj996  30725  bnj1021  30734  bnj1033  30737  ellines  31874
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