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Theorem sylani 635
Description: A syllogism inference. (Contributed by NM, 2-May-1996.)
Hypotheses
Ref Expression
sylani.1  |-  ( ph  ->  ch )
sylani.2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
sylani  |-  ( ps 
->  ( ( ph  /\  th )  ->  ta )
)

Proof of Theorem sylani
StepHypRef Expression
1 sylani.1 . . 3  |-  ( ph  ->  ch )
21a1i 10 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
3 sylani.2 . 2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3syland 467 1  |-  ( ps 
->  ( ( ph  /\  th )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  syl2ani  637  inf3lem2  7346  zorn2lem5  8143  uzwo  10297  uzwoOLD  10298  supxrun  10650  csmdsymi  22930  pmapjoin  30663
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
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