MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.501 Unicode version

Theorem pm5.501 332
Description: Theorem *5.501 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.501  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )

Proof of Theorem pm5.501
StepHypRef Expression
1 pm5.1im 231 . 2  |-  ( ph  ->  ( ps  ->  ( ph 
<->  ps ) ) )
2 bi1 180 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ph  ->  ps ) )
32com12 29 . 2  |-  ( ph  ->  ( ( ph  <->  ps )  ->  ps ) )
41, 3impbid 185 1  |-  ( ph  ->  ( ps  <->  ( ph  <->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  ibib  333  ibibr  334  nbn2  336  pm5.18  347  biass  350  pm5.1  833  sadadd2lem2  12568  isclo  16751  nrmmetd  18024
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179
  Copyright terms: Public domain W3C validator