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

Theorem exrot3 1801
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 1800 . 2  |-  ( E. x E. y E. z ph  <->  E. z E. y E. x ph )
2 excom 1798 . 2  |-  ( E. z E. y E. x ph  <->  E. y E. z E. x ph )
31, 2bitri 249 1  |-  ( E. x E. y E. z ph  <->  E. y E. z E. x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-11 1791
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  opabn0  4783  dmoprab  6377  rnoprab  6379  xpassen  7621  elima4  29104  brimg  29482  ellines  29697
  Copyright terms: Public domain W3C validator