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Theorem imbi1 313
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 19 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi1d 308 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  imbi1i  315  3impexpVD  28632  ancomsimpVD  28641  onfrALTVD  28667  hbimpgVD  28680  hbexgVD  28682  a9e2ndeqVD  28685  a9e2ndeqALT  28708
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 177
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