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Theorem imbi1 325
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 23 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi1d 319 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 189
This theorem is referenced by:  imbi1i  327  wl-nanbi1  31813  wl-nanbi2  31814  ifpbi1  36085  3impexpVD  37157  ancomstVD  37167  onfrALTVD  37193  hbimpgVD  37206  hbexgVD  37208  ax6e2ndeqVD  37211  ax6e2ndeqALT  37233
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