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Theorem syld3an2 1263
Description: A syllogism inference. (Contributed by NM, 20-May-2007.)
Hypotheses
Ref Expression
syld3an2.1  |-  ( (
ph  /\  ch  /\  th )  ->  ps )
syld3an2.2  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
Assertion
Ref Expression
syld3an2  |-  ( (
ph  /\  ch  /\  th )  ->  ta )

Proof of Theorem syld3an2
StepHypRef Expression
1 syld3an2.1 . . . 4  |-  ( (
ph  /\  ch  /\  th )  ->  ps )
213com23 1187 . . 3  |-  ( (
ph  /\  th  /\  ch )  ->  ps )
3 syld3an2.2 . . . 4  |-  ( (
ph  /\  ps  /\  th )  ->  ta )
433com23 1187 . . 3  |-  ( (
ph  /\  th  /\  ps )  ->  ta )
52, 4syld3an3 1261 . 2  |-  ( (
ph  /\  th  /\  ch )  ->  ta )
653com23 1187 1  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 962
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 964
This theorem is referenced by:  nppcan2  8005  nnncan  8009  nnncan2  8011  ltdivmul  8646  ledivmul  8647  ltdiv23  8662  lediv23  8663  dvdssub2  11546  dvdsgcdb  11712  lcmdvdsb  11776
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