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Theorem uunT11p1 41904
 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
uunT11p1.1 ((𝜑 ∧ ⊤ ∧ 𝜑) → 𝜓)
Assertion
Ref Expression
uunT11p1 (𝜑𝜓)

Proof of Theorem uunT11p1
StepHypRef Expression
1 3anrot 1097 . . . 4 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ 𝜑𝜑))
2 3anass 1092 . . . 4 ((⊤ ∧ 𝜑𝜑) ↔ (⊤ ∧ (𝜑𝜑)))
3 truan 1549 . . . 4 ((⊤ ∧ (𝜑𝜑)) ↔ (𝜑𝜑))
41, 2, 33bitri 300 . . 3 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ (𝜑𝜑))
5 anidm 568 . . 3 ((𝜑𝜑) ↔ 𝜑)
64, 5bitri 278 . 2 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ 𝜑)
7 uunT11p1.1 . 2 ((𝜑 ∧ ⊤ ∧ 𝜑) → 𝜓)
86, 7sylbir 238 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1084  ⊤wtru 1539 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 1086  df-tru 1541 This theorem is referenced by: (None)
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