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Theorem uunTT1p1 42095
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
uunTT1p1.1 ((⊤ ∧ 𝜑 ∧ ⊤) → 𝜓)
Assertion
Ref Expression
uunTT1p1 (𝜑𝜓)

Proof of Theorem uunTT1p1
StepHypRef Expression
1 3ancomb 1101 . . . 4 ((⊤ ∧ 𝜑 ∧ ⊤) ↔ (⊤ ∧ ⊤ ∧ 𝜑))
2 3anass 1097 . . . 4 ((⊤ ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ (⊤ ∧ 𝜑)))
3 anabs5 663 . . . 4 ((⊤ ∧ (⊤ ∧ 𝜑)) ↔ (⊤ ∧ 𝜑))
41, 2, 33bitri 300 . . 3 ((⊤ ∧ 𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑))
5 truan 1554 . . 3 ((⊤ ∧ 𝜑) ↔ 𝜑)
64, 5bitri 278 . 2 ((⊤ ∧ 𝜑 ∧ ⊤) ↔ 𝜑)
7 uunTT1p1.1 . 2 ((⊤ ∧ 𝜑 ∧ ⊤) → 𝜓)
86, 7sylbir 238 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1089  wtru 1544
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 210  df-an 400  df-3an 1091  df-tru 1546
This theorem is referenced by: (None)
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