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Theorem exrot3 2172
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 2171 . 2 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑧𝑦𝑥𝜑)
2 excom 2169 . 2 (∃𝑧𝑦𝑥𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
31, 2bitri 278 1 (∃𝑥𝑦𝑧𝜑 ↔ ∃𝑦𝑧𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wex 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-11 2161
This theorem depends on definitions:  df-bi 210  df-ex 1787
This theorem is referenced by:  opabn0  5409  dmoprab  7270  rnoprab  7272  xpassen  8661  cnvoprabOLD  30630  elima4  33322  brimg  33877  ellines  34092  rnxrn  36144  fundcmpsurinj  44387
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