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Theorem dissym1 32059
Description: A symmetry with .

See negsym1 32055 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
dissym1 ((𝜓 ∨ (𝜓 ∨ ⊥)) → (𝜓𝜑))

Proof of Theorem dissym1
StepHypRef Expression
1 orc 400 . 2 (𝜓 → (𝜓𝜑))
2 falim 1495 . . 3 (⊥ → 𝜑)
32orim2i 540 . 2 ((𝜓 ∨ ⊥) → (𝜓𝜑))
41, 3jaoi 394 1 ((𝜓 ∨ (𝜓 ∨ ⊥)) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wo 383  wfal 1485
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-or 385  df-tru 1483  df-fal 1486
This theorem is referenced by: (None)
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