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Theorem exp3acom23g 1361
Description: Implication form of exp3acom23 1362. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.
Assertion
Ref Expression
exp3acom23g  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ch  ->  ( ps  ->  th ) ) ) )

Proof of Theorem exp3acom23g
StepHypRef Expression
1 ancomsimp 1359 . . 3  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ( ch  /\  ps )  ->  th ) )
2 impexp 433 . . 3  |-  ( ( ( ch  /\  ps )  ->  th )  <->  ( ch  ->  ( ps  ->  th )
) )
31, 2bitri 240 . 2  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ch  ->  ( ps  ->  th )
) )
43imbi2i 303 1  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ch  ->  ( ps  ->  th ) ) ) )
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