Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e201 Structured version   Visualization version   GIF version

Theorem e201 41287
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e201.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e201.2 𝜃
e201.3 (   𝜑   ▶   𝜏   )
e201.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e201 (   𝜑   ,   𝜓   ▶   𝜂   )

Proof of Theorem e201
StepHypRef Expression
1 e201.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e201.2 . . 3 𝜃
32vd01 41223 . 2 (   𝜑   ▶   𝜃   )
4 e201.3 . 2 (   𝜑   ▶   𝜏   )
5 e201.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
61, 3, 4, 5e211 41283 1 (   𝜑   ,   𝜓   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 41195  (   wvd2 41203
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-vd1 41196  df-vd2 41204
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator