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Theorem eel00cT 39522
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel00cT.1 𝜑
eel00cT.2 𝜓
eel00cT.3 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
eel00cT (⊤ → 𝜒)

Proof of Theorem eel00cT
StepHypRef Expression
1 eel00cT.2 . . 3 𝜓
2 eel00cT.1 . . . 4 𝜑
3 eel00cT.3 . . . 4 ((𝜑𝜓) → 𝜒)
42, 3mpan 670 . . 3 (𝜓𝜒)
51, 4ax-mp 5 . 2 𝜒
65a1i 11 1 (⊤ → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wtru 1632
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 383
This theorem is referenced by: (None)
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