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Theorem uunTT1p2 41284
 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
uunTT1p2.1 ((𝜑 ∧ ⊤ ∧ ⊤) → 𝜓)
Assertion
Ref Expression
uunTT1p2 (𝜑𝜓)

Proof of Theorem uunTT1p2
StepHypRef Expression
1 3anrot 1096 . . . 4 ((𝜑 ∧ ⊤ ∧ ⊤) ↔ (⊤ ∧ ⊤ ∧ 𝜑))
2 3anass 1091 . . . 4 ((⊤ ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ (⊤ ∧ 𝜑)))
3 anabs5 661 . . . 4 ((⊤ ∧ (⊤ ∧ 𝜑)) ↔ (⊤ ∧ 𝜑))
41, 2, 33bitri 299 . . 3 ((𝜑 ∧ ⊤ ∧ ⊤) ↔ (⊤ ∧ 𝜑))
5 truan 1548 . . 3 ((⊤ ∧ 𝜑) ↔ 𝜑)
64, 5bitri 277 . 2 ((𝜑 ∧ ⊤ ∧ ⊤) ↔ 𝜑)
7 uunTT1p2.1 . 2 ((𝜑 ∧ ⊤ ∧ ⊤) → 𝜓)
86, 7sylbir 237 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083  ⊤wtru 1538 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 209  df-an 399  df-3an 1085  df-tru 1540 This theorem is referenced by: (None)
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