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Theorem syld3an1 1228
Description: A syllogism inference. (Contributed by NM, 7-Jul-2008.)
Hypotheses
Ref Expression
syld3an1.1  |-  ( ( ch  /\  ps  /\  th )  ->  ph )
syld3an1.2  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Assertion
Ref Expression
syld3an1  |-  ( ( ch  /\  ps  /\  th )  ->  ta )

Proof of Theorem syld3an1
StepHypRef Expression
1 syld3an1.1 . . . 4  |-  ( ( ch  /\  ps  /\  th )  ->  ph )
213com13 1156 . . 3  |-  ( ( th  /\  ps  /\  ch )  ->  ph )
3 syld3an1.2 . . . 4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
433com13 1156 . . 3  |-  ( ( th  /\  ps  /\  ph )  ->  ta )
52, 4syld3an3 1227 . 2  |-  ( ( th  /\  ps  /\  ch )  ->  ta )
653com13 1156 1  |-  ( ( ch  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  npncan  9069  ppncan  9089  div2neg  9483  ltmuldiv  9626  spwpr4  14340  zndvds  16503  subdivcomb1  24090  sigarexp  27849  atlrelat1  29511  cvlatcvr1  29531  dih11  31455
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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