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Theorem sylani 403
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 9 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
3 sylani.2 . 2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3syland 291 1  |-  ( ps 
->  ( ( ph  /\  th )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  syl2ani  405  fiintim  6817  lcmdvds  11773
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