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Theorem syl6c 63
Description: Inference combining syl6 32 with contraction. (Contributed by Alan Sare, 2-May-2011.)
Hypotheses
Ref Expression
syl6c.1  |-  ( ph  ->  ( ps  ->  ch ) )
syl6c.2  |-  ( ph  ->  ( ps  ->  th )
)
syl6c.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
syl6c  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem syl6c
StepHypRef Expression
1 syl6c.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
2 syl6c.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 syl6c.3 . . 3  |-  ( ch 
->  ( th  ->  ta ) )
42, 3syl6 32 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ta ) ) )
51, 4mpdd 39 1  |-  ( ph  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  syldd  64  impbidd  183  pm5.21ndd  345  jcad  521  ee22  1372  zorn2lem6  8383  sqreulem  12165  ontopbas  26180  ontgval  26183  ordtoplem  26187  ordcmp  26199
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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