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Theorem consym1 33665
Description: A symmetry with .

See negsym1 33662 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 1545 . . 3 (⊥ → ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑)))
21ad2antll 725 . 2 ((𝜓 ∧ (𝜓 ∧ ⊥)) → ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑)))
32pm2.43i 52 1 ((𝜓 ∧ (𝜓 ∧ ⊥)) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  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-an 397  df-tru 1531  df-fal 1541
This theorem is referenced by: (None)
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