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Theorem exrot3 2085
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 2084 . 2 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑧𝑦𝑥𝜑)
2 excom 2082 . 2 (∃𝑧𝑦𝑥𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
31, 2bitri 264 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-11 2074
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by:  opabn0  5035  dmoprab  6783  rnoprab  6785  xpassen  8095  cnvoprabOLD  29626  elima4  31803  brimg  32169  ellines  32384  rnxrn  34296
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