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Theorem syl3anl2 1267
Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
syl3anl2.1  |-  ( ph  ->  ch )
syl3anl2.2  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ta )  ->  et )
Assertion
Ref Expression
syl3anl2  |-  ( ( ( ps  /\  ph  /\ 
th )  /\  ta )  ->  et )

Proof of Theorem syl3anl2
StepHypRef Expression
1 syl3anl2.1 . . 3  |-  ( ph  ->  ch )
2 syl3anl2.2 . . . 4  |-  ( ( ( ps  /\  ch  /\ 
th )  /\  ta )  ->  et )
32ex 434 . . 3  |-  ( ( ps  /\  ch  /\  th )  ->  ( ta  ->  et ) )
41, 3syl3an2 1252 . 2  |-  ( ( ps  /\  ph  /\  th )  ->  ( ta  ->  et ) )
54imp 429 1  |-  ( ( ( ps  /\  ph  /\ 
th )  /\  ta )  ->  et )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 965
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 185  df-an 371  df-3an 967
This theorem is referenced by:  syl3anr2  1271  2atlt  33083
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