NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  excom13 GIF version

Theorem excom13 1743
Description: Swap 1st and 3rd existential quantifiers. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
excom13 (xyzφzyxφ)

Proof of Theorem excom13
StepHypRef Expression
1 excom 1741 . 2 (xyzφyxzφ)
2 excom 1741 . . 3 (xzφzxφ)
32exbii 1582 . 2 (yxzφyzxφ)
4 excom 1741 . 2 (yzxφzyxφ)
51, 3, 43bitri 262 1 (xyzφzyxφ)
Colors of variables: wff setvar class
Syntax hints:  wb 176  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  exrot3  1744  exrot4  1745
  Copyright terms: Public domain W3C validator