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Theorem consym1 32394
Description: A symmetry with .

See negsym1 32391 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion
Ref Expression
consym1 ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑))

Proof of Theorem consym1
StepHypRef Expression
1 falim 1496 . . 3 (⊥ → ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑)))
21ad2antll 764 . 2 ((𝜓 ∧ (𝜓 ∧ ⊥)) → ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑)))
32pm2.43i 52 1 ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wfal 1486
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-tru 1484  df-fal 1487
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator