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Theorem sylan2i 636
Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.)
Hypotheses
Ref Expression
sylan2i.1  |-  ( ph  ->  th )
sylan2i.2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
sylan2i  |-  ( ps 
->  ( ( ch  /\  ph )  ->  ta )
)

Proof of Theorem sylan2i
StepHypRef Expression
1 sylan2i.1 . . 3  |-  ( ph  ->  th )
21a1i 10 . 2  |-  ( ps 
->  ( ph  ->  th )
)
3 sylan2i.2 . 2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3sylan2d 468 1  |-  ( ps 
->  ( ( ch  /\  ph )  ->  ta )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  syl2ani  637  odi  6593  pssnn  7097  noinfepOLD  7377  ltexprlem7  8682  ltaprlem  8684  sup2  9726  filufint  17631  pjnormssi  22764  pellex  27023
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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