Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e22 Structured version   Visualization version   GIF version

Theorem e22 43365
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e22.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e22.2 (   𝜑   ,   𝜓   ▶   𝜃   )
e22.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
e22 (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e22
StepHypRef Expression
1 e22.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e22.2 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
3 e22.3 . . 3 (𝜒 → (𝜃𝜏))
43a1i 11 . 2 (𝜒 → (𝜒 → (𝜃𝜏)))
51, 1, 2, 4e222 43330 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 43271
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 206  df-an 398  df-vd2 43272
This theorem is referenced by:  e22an  43366  e02  43391  e12  43418  e20  43421  e21  43424  sspwtr  43515  pwtrVD  43518  pwtrrVD  43519  elex22VD  43533  tpid3gVD  43536  en3lplem2VD  43538  imbi12VD  43567  truniALTVD  43572  trintALTVD  43574  onfrALTlem3VD  43581  onfrALTlem2VD  43583  ax6e2eqVD  43601  ax6e2ndeqVD  43603  sb5ALTVD  43607
  Copyright terms: Public domain W3C validator