Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  un01 Structured version   Visualization version   GIF version

Theorem un01 42082
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 1547 . . . 4
21jctl 527 . . 3 (𝜑 → (⊤ ∧ 𝜑))
3 un01.1 . . . 4 (   (      ,   𝜑   )   ▶   𝜓   )
43dfvd2ani 41876 . . 3 ((⊤ ∧ 𝜑) → 𝜓)
52, 4syl 17 . 2 (𝜑𝜓)
65dfvd1ir 41866 1 (   𝜑   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wa 399  wtru 1544  (   wvd1 41862  (   wvhc2 41873
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-tru 1546  df-vd1 41863  df-vhc2 41874
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator