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Theorem imbi2 314
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 19 . 2  |-  ( (
ph 
<->  ps )  ->  ( ph 
<->  ps ) )
21imbi2d 307 1  |-  ( (
ph 
<->  ps )  ->  (
( ch  ->  ph )  <->  ( ch  ->  ps )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  3impexpbicom  1357  relexpindlem  24036  relexpind  24037  sbcim2g  28302  3impexpbicomVD  28633  sbcim2gVD  28651  csbeq2gVD  28668  con5VD  28676  hbexgVD  28682  a9e2ndeqVD  28685  2sb5ndVD  28686  a9e2ndeqALT  28708  2sb5ndALT  28709
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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