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Theorem syl6ci 1421
Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012.)
Hypotheses
Ref Expression
syl6ci.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl6ci.2  |-  ( ph  ->  th )
syl6ci.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
syl6ci  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem syl6ci
StepHypRef Expression
1 syl6ci.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 syl6ci.2 . . 3  |-  ( ph  ->  th )
32a1d 22 . 2  |-  ( ph  ->  ( ps  ->  th )
)
4 syl6ci.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4syl6c 66 1  |-  ( ph  ->  ( ps  ->  ta ) )
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:  ltxrlt  7844  ltnsym  7864  absle  10875  isumrpcl  11277
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