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Theorem exbir 1355
Description: Exportation implication also converting head from biconditional to conditional. This proof is exbirVD 28945 automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.
Assertion
Ref Expression
exbir  |-  ( ( ( ph  /\  ps )  ->  ( ch  <->  th )
)  ->  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) ) )

Proof of Theorem exbir
StepHypRef Expression
1 bi2 189 . . 3  |-  ( ( ch  <->  th )  ->  ( th  ->  ch ) )
21imim2i 13 . 2  |-  ( ( ( ph  /\  ps )  ->  ( ch  <->  th )
)  ->  ( ( ph  /\  ps )  -> 
( th  ->  ch ) ) )
32exp3a 425 1  |-  ( ( ( ph  /\  ps )  ->  ( ch  <->  th )
)  ->  ( ph  ->  ( ps  ->  ( th  ->  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
  Copyright terms: Public domain W3C validator