Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e03 Structured version   Visualization version   GIF version

Theorem e03 40951
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e03.1 𝜑
e03.2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
e03.3 (𝜑 → (𝜏𝜂))
Assertion
Ref Expression
e03 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e03
StepHypRef Expression
1 e03.1 . . 3 𝜑
21vd03 40810 . 2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )
3 e03.2 . 2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
4 e03.3 . 2 (𝜑 → (𝜏𝜂))
52, 3, 4e33 40945 1 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 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-3an 1081  df-vd3 40801
This theorem is referenced by:  e03an  40953  suctrALT2VD  41047
  Copyright terms: Public domain W3C validator