Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e3 Structured version   Visualization version   GIF version

Theorem e3 39489
Description: Meta-connective form of syl8 76. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e3.2 (𝜃𝜏)
Assertion
Ref Expression
e3 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e3
StepHypRef Expression
1 e3.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e3.2 . . 3 (𝜃𝜏)
32a1i 11 . 2 (𝜃 → (𝜃𝜏))
41, 1, 3e33 39486 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 39328
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 197  df-an 383  df-3an 1073  df-vd3 39331
This theorem is referenced by:  e3bi  39490  e3bir  39491  truniALTVD  39636  onfrALTlem2VD  39647
  Copyright terms: Public domain W3C validator