MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exrot3 Unicode version

Theorem exrot3 1755
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exrot3  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )

Proof of Theorem exrot3
StepHypRef Expression
1 excom13 1754 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1752 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 241 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   E.wex 1547
This theorem is referenced by:  opabn0  4445  dmoprab  6113  rnoprab  6115  xpassen  7161  brimg  25690  ellines  25990
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-7 1745
This theorem depends on definitions:  df-bi 178  df-ex 1548
  Copyright terms: Public domain W3C validator