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Theorem syl3anl3 1232
Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
syl3anl3.1  |-  ( ph  ->  th )
syl3anl3.2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ta )  ->  et )
Assertion
Ref Expression
syl3anl3  |-  ( ( ( ps  /\  ch  /\ 
ph )  /\  ta )  ->  et )

Proof of Theorem syl3anl3
StepHypRef Expression
1 syl3anl3.1 . . 3  |-  ( ph  ->  th )
213anim3i 1139 . 2  |-  ( ( ps  /\  ch  /\  ph )  ->  ( ps  /\ 
ch  /\  th )
)
3 syl3anl3.2 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ta )  ->  et )
42, 3sylan 457 1  |-  ( ( ( ps  /\  ch  /\ 
ph )  /\  ta )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  lgsdirnn0  20594  atcvreq0  30126  paddasslem16  30646
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
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