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Theorem an31s 504
Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006.)
Hypothesis
Ref Expression
an32s.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
an31s  |-  ( ( ( ch  /\  ps )  /\  ph )  ->  th )

Proof of Theorem an31s
StepHypRef Expression
1 an32s.1 . . . 4  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
21exp31 346 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32com13 74 . 2  |-  ( ch 
->  ( ps  ->  ( ph  ->  th ) ) )
43imp31 243 1  |-  ( ( ( ch  /\  ps )  /\  ph )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem is referenced by:  genpassl  6620  genpassu  6621
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