Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  imsym1 Structured version   Visualization version   GIF version

Theorem imsym1 33664
Description: A symmetry with .

See negsym1 33663 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
imsym1 ((𝜓 → (𝜓 → ⊥)) → (𝜓𝜑))

Proof of Theorem imsym1
StepHypRef Expression
1 pm2.21 123 . 2 𝜓 → (𝜓𝜑))
2 falim 1545 . . 3 (⊥ → 𝜑)
32imim2i 16 . 2 ((𝜓 → ⊥) → (𝜓𝜑))
41, 3ja 187 1 ((𝜓 → (𝜓 → ⊥)) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1540
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 208  df-tru 1531  df-fal 1541
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator