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Theorem eel000cT 38754
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel000cT.1 𝜑
eel000cT.2 𝜓
eel000cT.3 𝜒
eel000cT.4 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
eel000cT (⊤ → 𝜃)

Proof of Theorem eel000cT
StepHypRef Expression
1 eel000cT.3 . . 3 𝜒
2 eel000cT.2 . . . 4 𝜓
3 eel000cT.1 . . . . 5 𝜑
4 eel000cT.4 . . . . 5 ((𝜑𝜓𝜒) → 𝜃)
53, 4mp3an1 1410 . . . 4 ((𝜓𝜒) → 𝜃)
62, 5mpan 706 . . 3 (𝜒𝜃)
71, 6ax-mp 5 . 2 𝜃
87a1i 11 1 (⊤ → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1037  wtru 1483
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-3an 1039
This theorem is referenced by: (None)
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