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Theorem syld3an1 1279
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 1203 . . 3  |-  ( ( th  /\  ps  /\  ch )  ->  ph )
3 syld3an1.2 . . . 4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
433com13 1203 . . 3  |-  ( ( th  /\  ps  /\  ph )  ->  ta )
52, 4syld3an3 1278 . 2  |-  ( ( th  /\  ps  /\  ch )  ->  ta )
653com13 1203 1  |-  ( ( ch  /\  ps  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 973
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 975
This theorem is referenced by:  tfrcllembacc  6334  npncan  8140  nnpcan  8142  ppncan  8161  muldivdirap  8624  div2negap  8652  ltmuldiv  8790  mulqmod0  10286
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