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Theorem eel0TT 38408
 Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel0TT.1 𝜑
eel0TT.2 (⊤ → 𝜓)
eel0TT.3 (⊤ → 𝜒)
eel0TT.4 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
eel0TT 𝜃

Proof of Theorem eel0TT
StepHypRef Expression
1 eel0TT.3 . . 3 (⊤ → 𝜒)
2 truan 1498 . . . 4 ((⊤ ∧ 𝜒) ↔ 𝜒)
3 eel0TT.2 . . . . 5 (⊤ → 𝜓)
4 eel0TT.1 . . . . . 6 𝜑
5 eel0TT.4 . . . . . 6 ((𝜑𝜓𝜒) → 𝜃)
64, 5mp3an1 1408 . . . . 5 ((𝜓𝜒) → 𝜃)
73, 6sylan 488 . . . 4 ((⊤ ∧ 𝜒) → 𝜃)
82, 7sylbir 225 . . 3 (𝜒𝜃)
91, 8syl 17 . 2 (⊤ → 𝜃)
109trud 1490 1 𝜃
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1036  ⊤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-3an 1038  df-tru 1483 This theorem is referenced by: (None)
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