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Theorem syl3anr2 1317
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 454 . . 3  |-  ( ( ( ps  /\  th  /\  ta )  /\  ch )  ->  et )
41, 3syl3anl2 1313 . 2  |-  ( ( ( ps  /\  ph  /\ 
ta )  /\  ch )  ->  et )
54ancoms 454 1  |-  ( ( ch  /\  ( ps 
/\  ph  /\  ta )
)  ->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    /\ w3a 982
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984
This theorem is referenced by:  mulgsubdir  16740  vcsubdir  26020  dipassr2  26333
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