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Theorem syli 37
Description: Syllogism inference with common nested antecedent. (Contributed by NM, 4-Nov-2004.)
Hypotheses
Ref Expression
syli.1  |-  ( ps 
->  ( ph  ->  ch ) )
syli.2  |-  ( ch 
->  ( ph  ->  th )
)
Assertion
Ref Expression
syli  |-  ( ps 
->  ( ph  ->  th )
)

Proof of Theorem syli
StepHypRef Expression
1 syli.1 . 2  |-  ( ps 
->  ( ph  ->  ch ) )
2 syli.2 . . 3  |-  ( ch 
->  ( ph  ->  th )
)
32com12 30 . 2  |-  ( ph  ->  ( ch  ->  th )
)
41, 3sylcom 28 1  |-  ( ps 
->  ( ph  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  ibd  177  bijadc  867  sbi2v  1864  elab3gf  2834  elreldm  4765  tz6.12c  5451  rntpos  6154  smores  6189  f1domg  6652  negm  9414
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