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Theorem bj-imbi12 30747
Description: Imported form (uncurried form) of imbi12 322. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-imbi12  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )
)  ->  ( ( ph  ->  ch )  <->  ( ps  ->  th ) ) )

Proof of Theorem bj-imbi12
StepHypRef Expression
1 imbi12 322 . 2  |-  ( (
ph 
<->  ps )  ->  (
( ch  <->  th )  ->  ( ( ph  ->  ch )  <->  ( ps  ->  th ) ) ) )
21imp 429 1  |-  ( ( ( ph  <->  ps )  /\  ( ch  <->  th )
)  ->  ( ( ph  ->  ch )  <->  ( ps  ->  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 186    /\ wa 369
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 187  df-an 371
This theorem is referenced by: (None)
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