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Theorem sylanl1 394
Description: A syllogism inference. (Contributed by NM, 10-Mar-2005.)
Hypotheses
Ref Expression
sylanl1.1  |-  ( ph  ->  ps )
sylanl1.2  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
sylanl1  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )

Proof of Theorem sylanl1
StepHypRef Expression
1 sylanl1.1 . . 3  |-  ( ph  ->  ps )
21anim1i 333 . 2  |-  ( (
ph  /\  ch )  ->  ( ps  /\  ch ) )
3 sylanl1.2 . 2  |-  ( ( ( ps  /\  ch )  /\  th )  ->  ta )
42, 3sylan 277 1  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  adantlll  464  adantllr  465  isocnv  5530  mapxpen  6494  nqnq0pi  6900  nqpnq0nq  6915  addnqprl  6991  addnqpru  6992
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