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Theorem sylancbr 603
Description: A syllogism inference combined with contraction. (Contributed by NM, 3-Sep-2004.)
Hypotheses
Ref Expression
sylancbr.1 (𝜓𝜑)
sylancbr.2 (𝜒𝜑)
sylancbr.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
sylancbr (𝜑𝜃)

Proof of Theorem sylancbr
StepHypRef Expression
1 sylancbr.1 . . 3 (𝜓𝜑)
2 sylancbr.2 . . 3 (𝜒𝜑)
3 sylancbr.3 . . 3 ((𝜓𝜒) → 𝜃)
41, 2, 3syl2anbr 601 . 2 ((𝜑𝜑) → 𝜃)
54anidms 570 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  unixpid  6107
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