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Theorem 3exbii 1587
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 1585 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1586 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104  wex 1472
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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eeeanv  1913  ceqsex6v  2756  oprabid  5853  dfoprab2  5868  dftpos3  6209  xpassen  6775
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