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Theorem sylanr2 651
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr2.1  |-  ( ph  ->  th )
sylanr2.2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
sylanr2  |-  ( ( ps  /\  ( ch 
/\  ph ) )  ->  ta )

Proof of Theorem sylanr2
StepHypRef Expression
1 sylanr2.1 . . 3  |-  ( ph  ->  th )
21anim2i 567 . 2  |-  ( ( ch  /\  ph )  ->  ( ch  /\  th ) )
3 sylanr2.2 . 2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
42, 3sylan2 472 1  |-  ( ( ps  /\  ( ch 
/\  ph ) )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369
This theorem is referenced by:  adantrrl  721  adantrrr  722  1stconst  6861  2ndconst  6862  isfin7-2  8767  mulsub  9995  fzsubel  11723  expsub  12195  ramlb  14621  0ram  14622  ressmplvsca  18316  tgcl  19638  fgss2  20541  nmoid  21415  chirredlem4  27510  pridlc3  30710  stoweidlem34  32055
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