Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e022 Structured version   Visualization version   GIF version

Theorem e022 41271
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e022.1 𝜑
e022.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e022.3 (   𝜓   ,   𝜒   ▶   𝜏   )
e022.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e022 (   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e022
StepHypRef Expression
1 e022.1 . . 3 𝜑
21vd02 41228 . 2 (   𝜓   ,   𝜒   ▶   𝜑   )
3 e022.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
4 e022.3 . 2 (   𝜓   ,   𝜒   ▶   𝜏   )
5 e022.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
62, 3, 4, 5e222 41266 1 (   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 41207
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-vd2 41208
This theorem is referenced by:  onfrALTVD  41521
  Copyright terms: Public domain W3C validator