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Theorem an13s 532
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 357 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32com13 79 . 2  |-  ( ch 
->  ( ps  ->  ( ph  ->  th ) ) )
43imp32 253 1  |-  ( ( ch  /\  ( ps 
/\  ph ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by: (None)
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