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Theorem un01 39518
Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
un01.1 (   (      ,   𝜑   )   ▶   𝜓   )
Assertion
Ref Expression
un01 (   𝜑   ▶   𝜓   )

Proof of Theorem un01
StepHypRef Expression
1 tru 1636 . . . 4
21jctl 565 . . 3 (𝜑 → (⊤ ∧ 𝜑))
3 un01.1 . . . 4 (   (      ,   𝜑   )   ▶   𝜓   )
43dfvd2ani 39301 . . 3 ((⊤ ∧ 𝜑) → 𝜓)
52, 4syl 17 . 2 (𝜑𝜓)
65dfvd1ir 39291 1 (   𝜑   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wa 383  wtru 1633  (   wvd1 39287  (   wvhc2 39298
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 385  df-tru 1635  df-vd1 39288  df-vhc2 39299
This theorem is referenced by: (None)
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