MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  2exnexn Unicode version

Theorem 2exnexn 1572
Description: Theorem *11.51 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.) (Proof shortened by Wolf Lammen, 25-Sep-2014.)
Assertion
Ref Expression
2exnexn  |-  ( E. x A. y ph  <->  -. 
A. x E. y  -.  ph )

Proof of Theorem 2exnexn
StepHypRef Expression
1 alexn 1571 . 2  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )
21con2bii 324 1  |-  ( E. x A. y ph  <->  -. 
A. x E. y  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178   A.wal 1532   E.wex 1533
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549
This theorem depends on definitions:  df-bi 179  df-ex 1534
  Copyright terms: Public domain W3C validator