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

Theorem alex 1559
Description: Theorem 19.6 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
alex  |-  ( A. x ph  <->  -.  E. x  -.  ph )

Proof of Theorem alex
StepHypRef Expression
1 notnot 282 . . 3  |-  ( ph  <->  -. 
-.  ph )
21albii 1553 . 2  |-  ( A. x ph  <->  A. x  -.  -.  ph )
3 alnex 1530 . 2  |-  ( A. x  -.  -.  ph  <->  -.  E. x  -.  ph )
42, 3bitri 240 1  |-  ( A. x ph  <->  -.  E. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1527   E.wex 1528
This theorem is referenced by:  2nalexn  1560  exnal  1561  exists2  2233  pm10.253  27557  vk15.4j  28291  vk15.4jVD  28690
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
  Copyright terms: Public domain W3C validator