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Theorem sylsyld 57
Description: Virtual deduction rule. (Contributed by Alan Sare, 20-Apr-2011.)
Hypotheses
Ref Expression
sylsyld.1  |-  ( ph  ->  ps )
sylsyld.2  |-  ( ph  ->  ( ch  ->  th )
)
sylsyld.3  |-  ( ps 
->  ( th  ->  ta ) )
Assertion
Ref Expression
sylsyld  |-  ( ph  ->  ( ch  ->  ta ) )

Proof of Theorem sylsyld
StepHypRef Expression
1 sylsyld.2 . 2  |-  ( ph  ->  ( ch  ->  th )
)
2 sylsyld.1 . . 3  |-  ( ph  ->  ps )
3 sylsyld.3 . . 3  |-  ( ps 
->  ( th  ->  ta ) )
42, 3syl 14 . 2  |-  ( ph  ->  ( th  ->  ta ) )
51, 4syld 44 1  |-  ( ph  ->  ( ch  ->  ta ) )
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:  ax10o  1644  a16g  1786  trintssm  3899  funimaexglem  5013  smoiun  5950  findcard2  6423  ltexprlemrl  6862  archsr  7020  elfz0ubfz0  9213
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