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Theorem syl3anl3 1314
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 1193 . 2  |-  ( ( ps  /\  ch  /\  ph )  ->  ( ps  /\ 
ch  /\  th )
)
3 syl3anl3.2 . 2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ta )  ->  et )
42, 3sylan 473 1  |-  ( ( ( ps  /\  ch  /\ 
ph )  /\  ta )  ->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    /\ w3a 982
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 188  df-an 372  df-3an 984
This theorem is referenced by:  lgsdirnn0  24130  atcvreq0  32589  paddasslem16  33109
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