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Theorem mpisyl 1380
Description: A syllogism combined with a modus ponens inference. (Contributed by Alan Sare, 25-Jul-2011.)
Hypotheses
Ref Expression
mpisyl.1  |-  ( ph  ->  ps )
mpisyl.2  |-  ch
mpisyl.3  |-  ( ps 
->  ( ch  ->  th )
)
Assertion
Ref Expression
mpisyl  |-  ( ph  ->  th )

Proof of Theorem mpisyl
StepHypRef Expression
1 mpisyl.1 . 2  |-  ( ph  ->  ps )
2 mpisyl.2 . . 3  |-  ch
3 mpisyl.3 . . 3  |-  ( ps 
->  ( ch  ->  th )
)
42, 3mpi 15 . 2  |-  ( ps 
->  th )
51, 4syl 14 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  ceqsex  2657  reusv1  4278  fliftcnv  5566  fliftfun  5567  tfrlemibfn  6085  tfr1onlembfn  6101  tfrcllembfn  6114  cnvct  6516  ordiso  6719  exmidomni  6788  uzsinds  9836  fimaxq  10223  ltoddhalfle  11158  phicl2  11455
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