MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imbi1 Unicode version

Theorem imbi1 314
Description: Theorem *4.84 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
imbi1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )

Proof of Theorem imbi1
StepHypRef Expression
1 id 20 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi1d 309 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177
This theorem is referenced by:  imbi1i  316  3impexpVD  28677  ancomsimpVD  28686  onfrALTVD  28712  hbimpgVD  28725  hbexgVD  28727  a9e2ndeqVD  28730  a9e2ndeqALT  28753
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178
  Copyright terms: Public domain W3C validator