MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  an13s Unicode version

Theorem an13s 778
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)
Hypothesis
Ref Expression
an12s.1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
an13s  |-  ( ( ch  /\  ( ps 
/\  ph ) )  ->  th )

Proof of Theorem an13s
StepHypRef Expression
1 an12s.1 . . . 4  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
21exp32 588 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32com13 74 . 2  |-  ( ch 
->  ( ps  ->  ( ph  ->  th ) ) )
43imp32 422 1  |-  ( ( ch  /\  ( ps 
/\  ph ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  abfmpeld  23233
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