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Theorem uunT11p1 38492
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 1041 . . . 4 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ (⊤ ∧ 𝜑𝜑))
2 3anass 1040 . . . 4 ((⊤ ∧ 𝜑𝜑) ↔ (⊤ ∧ (𝜑𝜑)))
3 truan 1498 . . . 4 ((⊤ ∧ (𝜑𝜑)) ↔ (𝜑𝜑))
41, 2, 33bitri 286 . . 3 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ (𝜑𝜑))
5 anidm 675 . . 3 ((𝜑𝜑) ↔ 𝜑)
64, 5bitri 264 . 2 ((𝜑 ∧ ⊤ ∧ 𝜑) ↔ 𝜑)
7 uunT11p1.1 . 2 ((𝜑 ∧ ⊤ ∧ 𝜑) → 𝜓)
86, 7sylbir 225 1 (𝜑𝜓)
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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