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Theorem syl3anr1 1234
Description: A syllogism inference. (Contributed by NM, 31-Jul-2007.)
Hypotheses
Ref Expression
syl3anr1.1  |-  ( ph  ->  ps )
syl3anr1.2  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
Assertion
Ref Expression
syl3anr1  |-  ( ( ch  /\  ( ph  /\ 
th  /\  ta )
)  ->  et )

Proof of Theorem syl3anr1
StepHypRef Expression
1 syl3anr1.1 . . 3  |-  ( ph  ->  ps )
213anim1i 1138 . 2  |-  ( (
ph  /\  th  /\  ta )  ->  ( ps  /\  th 
/\  ta ) )
3 syl3anr1.2 . 2  |-  ( ( ch  /\  ( ps 
/\  th  /\  ta )
)  ->  et )
42, 3sylan2 460 1  |-  ( ( ch  /\  ( ph  /\ 
th  /\  ta )
)  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  btwnconn1lem4  24785  pridlc2  26800  atmod1i1  30668
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  df-3an 936
  Copyright terms: Public domain W3C validator