Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e00an Structured version   Visualization version   GIF version

Theorem e00an 39415
Description: Elimination rule identical to mp2an 710. The non-virtual deduction form is the virtual deduction form, which is mp2an 710. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e00an.1 𝜑
e00an.2 𝜓
e00an.3 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
e00an 𝜒

Proof of Theorem e00an
StepHypRef Expression
1 e00an.1 . 2 𝜑
2 e00an.2 . 2 𝜓
3 e00an.3 . 2 ((𝜑𝜓) → 𝜒)
41, 2, 3mp2an 710 1 𝜒
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 385
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator