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Theorem 3exbii 1543
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 1541 . 2 (∃𝑧𝜑 ↔ ∃𝑧𝜓)
322exbii 1542 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑥𝑦𝑧𝜓)
Colors of variables: wff set class
Syntax hints:  wb 103  wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  eeeanv  1856  ceqsex6v  2663  oprabid  5681  dfoprab2  5696  dftpos3  6027  xpassen  6546
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