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Theorem sylsyld 52
Description: Virtual deduction rule. (Contributed by Alan Sare, 20-Apr-2011.)
Hypotheses
Ref Expression
sylsyld.1 (φψ)
sylsyld.2 (φ → (χθ))
sylsyld.3 (ψ → (θτ))
Assertion
Ref Expression
sylsyld (φ → (χτ))

Proof of Theorem sylsyld
StepHypRef Expression
1 sylsyld.2 . 2 (φ → (χθ))
2 sylsyld.1 . . 3 (φψ)
3 sylsyld.3 . . 3 (ψ → (θτ))
42, 3syl 14 . 2 (φ → (θτ))
51, 4syld 40 1 (φ → (χτ))
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  1600  a16g  1741  trint0m  3862  funimaexglem  4925  smoiun  5857  ltexprlemrl  6583  archsr  6688  elfz0ubfz0  8732
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