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Theorem syl3anr2 1235
Description: A syllogism inference. (Contributed by NM, 1-Aug-2007.)
Hypotheses
Ref Expression
syl3anr2.1  |-  ( ph  ->  th )
syl3anr2.2  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
Assertion
Ref Expression
syl3anr2  |-  ( ( ch  /\  ( ps 
/\  ph  /\  ta )
)  ->  et )

Proof of Theorem syl3anr2
StepHypRef Expression
1 syl3anr2.1 . . 3  |-  ( ph  ->  th )
2 syl3anr2.2 . . . 4  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
32ancoms 439 . . 3  |-  ( ( ( ps  /\  th  /\  ta )  /\  ch )  ->  et )
41, 3syl3anl2 1231 . 2  |-  ( ( ( ps  /\  ph  /\ 
ta )  /\  ch )  ->  et )
54ancoms 439 1  |-  ( ( ch  /\  ( ps 
/\  ph  /\  ta )
)  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  mulgsubdir  14598  vcsubdir  21112  dipassr2  21425
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  df-3an 936
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