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Theorem eelT1 38415
Description: Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009.) (Revised by Alan Sare, 23-Dec-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelT1.1 (⊤ → 𝜑)
eelT1.2 (𝜓𝜒)
eelT1.3 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
eelT1 (𝜓𝜃)

Proof of Theorem eelT1
StepHypRef Expression
1 eelT1.1 . . 3 (⊤ → 𝜑)
21trud 1490 . 2 𝜑
3 eelT1.2 . 2 (𝜓𝜒)
4 eelT1.3 . 2 ((𝜑𝜒) → 𝜃)
52, 3, 4sylancr 694 1 (𝜓𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wtru 1481
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  df-tru 1483
This theorem is referenced by: (None)
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