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Theorem 3exbii 1571
Description: Inference adding 3 existential quantifiers to both sides of an equivalence. (Contributed by NM, 2-May-1995.)
Hypothesis
Ref Expression
exbii.1 (𝜑𝜓)
Assertion
Ref Expression
3exbii (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)

Proof of Theorem 3exbii
StepHypRef Expression
1 exbii.1 . . 3 (𝜑𝜓)
21exbii 1569 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1570 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104  wex 1453
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eeeanv  1885  ceqsex6v  2704  oprabid  5771  dfoprab2  5786  dftpos3  6127  xpassen  6692
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