MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp3acom23g Structured version   Unicode version

Theorem exp3acom23g 1381
Description: Implication form of exp3acom23 1382. (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 1379 . . 3  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ( ch  /\  ps )  ->  th ) )
2 impexp 435 . . 3  |-  ( ( ( ch  /\  ps )  ->  th )  <->  ( ch  ->  ( ps  ->  th )
) )
31, 2bitri 242 . 2  |-  ( ( ( ps  /\  ch )  ->  th )  <->  ( ch  ->  ( ps  ->  th )
) )
43imbi2i 305 1  |-  ( (
ph  ->  ( ( ps 
/\  ch )  ->  th )
)  <->  ( ph  ->  ( ch  ->  ( ps  ->  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ wa 360
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 179  df-an 362
  Copyright terms: Public domain W3C validator