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Theorem imsym1 31393
Description: A symmetry with .

See negsym1 31392 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

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

Proof of Theorem imsym1
StepHypRef Expression
1 pm2.21 118 . 2 𝜓 → (𝜓𝜑))
2 falim 1488 . . 3 (⊥ → 𝜑)
32imim2i 16 . 2 ((𝜓 → ⊥) → (𝜓𝜑))
41, 3ja 171 1 ((𝜓 → (𝜓 → ⊥)) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1479
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 195  df-tru 1477  df-fal 1480
This theorem is referenced by: (None)
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