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Theorem un10 42408
Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
un10.1 (   (   𝜑   ,      )   ▶   𝜓   )
Assertion
Ref Expression
un10 (   𝜑   ▶   𝜓   )

Proof of Theorem un10
StepHypRef Expression
1 tru 1543 . . . 4
21jctr 525 . . 3 (𝜑 → (𝜑 ∧ ⊤))
3 un10.1 . . . 4 (   (   𝜑   ,      )   ▶   𝜓   )
43dfvd2ani 42203 . . 3 ((𝜑 ∧ ⊤) → 𝜓)
52, 4syl 17 . 2 (𝜑𝜓)
65dfvd1ir 42193 1 (   𝜑   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wa 396  wtru 1540  (   wvd1 42189  (   wvhc2 42200
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 206  df-an 397  df-tru 1542  df-vd1 42190  df-vhc2 42201
This theorem is referenced by: (None)
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