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Theorem imbi1 315
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 21 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi1d 310 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178
This theorem is referenced by:  imbi1i  317  3impexpVD  27322  ancomsimpVD  27331  onfrALTVD  27357  hbimpgVD  27370  hbexgVD  27372  a9e2ndeqVD  27375  a9e2ndeqALT  27398
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
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