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Theorem sylan2i 659
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 11 . 2  |-  ( ps 
->  ( ph  ->  th )
)
3 sylan2i.2 . 2  |-  ( ps 
->  ( ( ch  /\  th )  ->  ta )
)
42, 3sylan2d 484 1  |-  ( ps 
->  ( ( ch  /\  ph )  ->  ta )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370
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 188  df-an 372
This theorem is referenced by:  syl2ani  660  odi  7288  pssnn  7796  ltexprlem7  9466  ltaprlem  9468  sup2  10565  filufint  20866  pjnormssi  27656  poimirlem27  31671  poimirlem31  31675  pellex  35389
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