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Theorem sylsyld 56
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 44 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  1619  a16g  1760  trintssm  3898  funimaexglem  5010  smoiun  5947  findcard2  6377  ltexprlemrl  6766  archsr  6924  elfz0ubfz0  9084
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