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

Theorem 2nalexn 1620
Description: Part of theorem *11.5 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2nalexn  |-  ( -. 
A. x A. y ph 
<->  E. x E. y  -.  ph )

Proof of Theorem 2nalexn
StepHypRef Expression
1 df-ex 1588 . . 3  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x  -.  E. y  -.  ph )
2 alex 1618 . . . 4  |-  ( A. y ph  <->  -.  E. y  -.  ph )
32albii 1611 . . 3  |-  ( A. x A. y ph  <->  A. x  -.  E. y  -.  ph )
41, 3xchbinxr 311 . 2  |-  ( E. x E. y  -. 
ph 
<->  -.  A. x A. y ph )
54bicomi 202 1  |-  ( -. 
A. x A. y ph 
<->  E. x E. y  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  spc2gv  3158  hashfun  12303  spc2d  25995  pm11.52  29779  2exanali  29780
  Copyright terms: Public domain W3C validator