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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  23408  relexpind  23409  sbcim2g  27355  3impexpbicomVD  27683  sbcim2gVD  27701  csbeq2gVD  27718  con5VD  27726  hbexgVD  27732  a9e2ndeqVD  27735  2sb5ndVD  27736  a9e2ndeqALT  27758  2sb5ndALT  27759
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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