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Theorem biimp 28545
Description: Importation inference similar to imp 418, except the outermost implication of the hypothesis is a biconditional. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
biimp.1  |-  ( ph  <->  ( ps  ->  ch )
)
Assertion
Ref Expression
biimp  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem biimp
StepHypRef Expression
1 biimp.1 . . 3  |-  ( ph  <->  ( ps  ->  ch )
)
21biimpi 186 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
32imp 418 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
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  df-an 360
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