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Theorem syl2ani 656
Description: A syllogism inference. (Contributed by NM, 3-Aug-1999.)
Hypotheses
Ref Expression
syl2ani.1  |-  ( ph  ->  ch )
syl2ani.2  |-  ( et 
->  th )
syl2ani.3  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
syl2ani  |-  ( ps 
->  ( ( ph  /\  et )  ->  ta )
)

Proof of Theorem syl2ani
StepHypRef Expression
1 syl2ani.1 . 2  |-  ( ph  ->  ch )
2 syl2ani.2 . . 3  |-  ( et 
->  th )
3 syl2ani.3 . . 3  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3sylan2i 655 . 2  |-  ( ps 
->  ( ( ch  /\  et )  ->  ta )
)
51, 4sylani 654 1  |-  ( ps 
->  ( ( ph  /\  et )  ->  ta )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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
This theorem is referenced by:  2mo  2369  frxp  6793  mapen  7586  fin1a2lem9  8689  psss  15504  mgmidmo  15538  aannenlem1  21928  funtransport  28207  cgrxfr  28231  btwnxfr  28232  bj-cbv3tb  32540
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