MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  imbi2 Unicode version

Theorem imbi2 316
Description: Theorem *4.85 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 19-May-2013.)
Assertion
Ref Expression
imbi2  |-  ( (
ph 
<->  ps )  ->  (
( ch  ->  ph )  <->  ( ch  ->  ps )
) )

Proof of Theorem imbi2
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi2d 309 1  |-  ( (
ph 
<->  ps )  ->  (
( ch  ->  ph )  <->  ( ch  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  3impexpbicom  1363  relexpindlem  23207  relexpind  23208  sbcim2g  26995  3impexpbicomVD  27323  sbcim2gVD  27341  csbeq2gVD  27358  con5VD  27366  hbexgVD  27372  a9e2ndeqVD  27375  2sb5ndVD  27376  a9e2ndeqALT  27398  2sb5ndALT  27399
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