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Theorem uunT12 41492
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
uunT12.1 ((⊤ ∧ 𝜑𝜓) → 𝜒)
Assertion
Ref Expression
uunT12 ((𝜑𝜓) → 𝜒)

Proof of Theorem uunT12
StepHypRef Expression
1 3anass 1092 . . 3 ((⊤ ∧ 𝜑𝜓) ↔ (⊤ ∧ (𝜑𝜓)))
2 truan 1549 . . 3 ((⊤ ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
31, 2bitri 278 . 2 ((⊤ ∧ 𝜑𝜓) ↔ (𝜑𝜓))
4 uunT12.1 . 2 ((⊤ ∧ 𝜑𝜓) → 𝜒)
53, 4sylbir 238 1 ((𝜑𝜓) → 𝜒)
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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