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Theorem sylanr2 634
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 552 . 2  |-  ( ( ch  /\  ph )  ->  ( ch  /\  th ) )
3 sylanr2.2 . 2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
42, 3sylan2 460 1  |-  ( ( ps  /\  ( ch 
/\  ph ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  adantrrl  704  adantrrr  705  1stconst  6223  2ndconst  6224  isfin7-2  8038  mulsub  9238  fzsubel  10843  expsub  11165  ramlb  13082  0ram  13083  ressmplvsca  16219  tgcl  16723  fgss2  17585  nmoid  18267  chirredlem4  22989  pridlc3  26801
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
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