Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e33 Structured version   Visualization version   GIF version

Theorem e33 44731
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e33.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e33.2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
e33.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
e33 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e33
StepHypRef Expression
1 e33.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e33.2 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
3 e33.3 . . 3 (𝜃 → (𝜏𝜂))
43a1i 11 . 2 (𝜃 → (𝜃 → (𝜏𝜂)))
51, 1, 2, 4e333 44730 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 44584
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 207  df-an 396  df-3an 1088  df-vd3 44587
This theorem is referenced by:  e33an  44732  e3  44734  e03  44737  e30  44741  e13  44745  e31  44748  e23  44752  e32  44755  truniALTVD  44875  trintALTVD  44877  onfrALTlem2VD  44886
  Copyright terms: Public domain W3C validator