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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  23440  relexpind  23441  sbcim2g  27573  3impexpbicomVD  27901  sbcim2gVD  27919  csbeq2gVD  27936  con5VD  27944  hbexgVD  27950  a9e2ndeqVD  27953  2sb5ndVD  27954  a9e2ndeqALT  27976  2sb5ndALT  27977
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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