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Theorem exrot3 1701
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 1700 . 2 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑧𝑦𝑥𝜑)
2 excom 1675 . 2 (∃𝑧𝑦𝑥𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
31, 2bitri 184 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wb 105  wex 1503
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  opabm  4298  rexiunxp  4787  dmoprab  5978  rnoprab  5980  cnvoprab  6260  xpassen  6857  dmaddpq  7409  dmmulpq  7410
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