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Theorem imbi1 321
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 22 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi1d 315 1  |-  ( (
ph 
<->  ps )  ->  (
( ph  ->  ch )  <->  ( ps  ->  ch )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184
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 185
This theorem is referenced by:  imbi1i  323  wl-nanbi1  31327  wl-nanbi2  31328  ifpbi1  35548  3impexpVD  36666  ancomstVD  36676  onfrALTVD  36702  hbimpgVD  36715  hbexgVD  36717  ax6e2ndeqVD  36720  ax6e2ndeqALT  36742
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