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Theorem un10 41006
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 1534 . . . 4
21jctr 525 . . 3 (𝜑 → (𝜑 ∧ ⊤))
3 un10.1 . . . 4 (   (   𝜑   ,      )   ▶   𝜓   )
43dfvd2ani 40801 . . 3 ((𝜑 ∧ ⊤) → 𝜓)
52, 4syl 17 . 2 (𝜑𝜓)
65dfvd1ir 40791 1 (   𝜑   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wa 396  wtru 1531  (   wvd1 40787  (   wvhc2 40798
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 208  df-an 397  df-tru 1533  df-vd1 40788  df-vhc2 40799
This theorem is referenced by: (None)
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