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Theorem uunTT1 38041
 Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uunTT1.1 ((⊤ ∧ ⊤ ∧ 𝜑) → 𝜓)
Assertion
Ref Expression
uunTT1 (𝜑𝜓)

Proof of Theorem uunTT1
StepHypRef Expression
1 3anass 1035 . . 3 ((⊤ ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ (⊤ ∧ 𝜑)))
2 anabs5 847 . . 3 ((⊤ ∧ (⊤ ∧ 𝜑)) ↔ (⊤ ∧ 𝜑))
3 truan 1492 . . 3 ((⊤ ∧ 𝜑) ↔ 𝜑)
41, 2, 33bitri 285 . 2 ((⊤ ∧ ⊤ ∧ 𝜑) ↔ 𝜑)
5 uunTT1.1 . 2 ((⊤ ∧ ⊤ ∧ 𝜑) → 𝜓)
64, 5sylbir 224 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031  ⊤wtru 1476 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 196  df-an 385  df-3an 1033  df-tru 1478 This theorem is referenced by: (None)
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