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Theorem syl3anr3 1271
Description: A syllogism inference. (Contributed by NM, 23-Aug-2007.)
Hypotheses
Ref Expression
syl3anr3.1  |-  ( ph  ->  ta )
syl3anr3.2  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
Assertion
Ref Expression
syl3anr3  |-  ( ( ch  /\  ( ps 
/\  th  /\  ph )
)  ->  et )

Proof of Theorem syl3anr3
StepHypRef Expression
1 syl3anr3.1 . . 3  |-  ( ph  ->  ta )
213anim3i 1170 . 2  |-  ( ( ps  /\  th  /\  ph )  ->  ( ps  /\ 
th  /\  ta )
)
3 syl3anr3.2 . 2  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
42, 3sylan2 284 1  |-  ( ( ch  /\  ( ps 
/\  th  /\  ph )
)  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by: (None)
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