Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e32an Structured version   Visualization version   GIF version

Theorem e32an 38807
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e32an.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e32an.2 (   𝜑   ,   𝜓   ▶   𝜏   )
e32an.3 ((𝜃𝜏) → 𝜂)
Assertion
Ref Expression
e32an (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e32an
StepHypRef Expression
1 e32an.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e32an.2 . 2 (   𝜑   ,   𝜓   ▶   𝜏   )
3 e32an.3 . . 3 ((𝜃𝜏) → 𝜂)
43ex 450 . 2 (𝜃 → (𝜏𝜂))
51, 2, 4e32 38805 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 384  (   wvd2 38613  (   wvd3 38623 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 386  df-3an 1038  df-vd2 38614  df-vd3 38626 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator