MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp41 Unicode version

Theorem exp41 593
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp41.1  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
exp41  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp41
StepHypRef Expression
1 exp41.1 . . 3  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
21ex 423 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( th  ->  ta ) )
32exp31 587 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  tz7.49  6457  supxrun  10634  branmfn  22685  1to3vfriswmgra  28185
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