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Theorem sylanr1 634
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr1.1  |-  ( ph  ->  ch )
sylanr1.2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
sylanr1  |-  ( ( ps  /\  ( ph  /\ 
th ) )  ->  ta )

Proof of Theorem sylanr1
StepHypRef Expression
1 sylanr1.1 . . 3  |-  ( ph  ->  ch )
21anim1i 552 . 2  |-  ( (
ph  /\  th )  ->  ( ch  /\  th ) )
3 sylanr1.2 . 2  |-  ( ( ps  /\  ( ch 
/\  th ) )  ->  ta )
42, 3sylan2 461 1  |-  ( ( ps  /\  ( ph  /\ 
th ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  adantrll  703  adantrlr  704  sbthlem9  7161  pczpre  13148  blsscls2  18424  rpvmasumlem  21048  leopmuli  23484  chirredlem1  23741  chirredlem3  23743  dvconstbi  27220  reccot  27847  rectan  27848
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 178  df-an 361
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