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Theorem sylancb 698
Description: A syllogism inference combined with contraction. (Contributed by NM, 3-Sep-2004.)
Hypotheses
Ref Expression
sylancb.1 (𝜑𝜓)
sylancb.2 (𝜑𝜒)
sylancb.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
sylancb (𝜑𝜃)

Proof of Theorem sylancb
StepHypRef Expression
1 sylancb.1 . . 3 (𝜑𝜓)
2 sylancb.2 . . 3 (𝜑𝜒)
3 sylancb.3 . . 3 ((𝜓𝜒) → 𝜃)
41, 2, 3syl2anb 496 . 2 ((𝜑𝜑) → 𝜃)
54anidms 676 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386
This theorem is referenced by: (None)
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