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Theorem syl3anl2 1233
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 424 . . 3  |-  ( ( ps  /\  ch  /\  th )  ->  ( ta  ->  et ) )
41, 3syl3an2 1218 . 2  |-  ( ( ps  /\  ph  /\  th )  ->  ( ta  ->  et ) )
54imp 419 1  |-  ( ( ( ps  /\  ph  /\ 
th )  /\  ta )  ->  et )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem is referenced by:  syl3anr2  1237  2atlt  29553
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  df-3an 938
  Copyright terms: Public domain W3C validator