Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  un10 Structured version   Visualization version   GIF version

Theorem un10 39540
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 1635 . . . 4
21jctr 514 . . 3 (𝜑 → (𝜑 ∧ ⊤))
3 un10.1 . . . 4 (   (   𝜑   ,      )   ▶   𝜓   )
43dfvd2ani 39324 . . 3 ((𝜑 ∧ ⊤) → 𝜓)
52, 4syl 17 . 2 (𝜑𝜓)
65dfvd1ir 39314 1 (   𝜑   ▶   𝜓   )
Colors of variables: wff setvar class
Syntax hints:  wa 382  wtru 1632  (   wvd1 39310  (   wvhc2 39321
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 383  df-tru 1634  df-vd1 39311  df-vhc2 39322
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator