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Theorem an13s 781
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 591 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32com13 76 . 2  |-  ( ch 
->  ( ps  ->  ( ph  ->  th ) ) )
43imp32 424 1  |-  ( ( ch  /\  ( ps 
/\  ph ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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