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Theorem bijust 194
Description: Theorem used to justify definition of biconditional df-bi 196. (Contributed by NM, 11-May-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)
Assertion
Ref Expression
bijust ¬ ((¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))) → ¬ (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))))

Proof of Theorem bijust
StepHypRef Expression
1 id 22 . 2 (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑)))
2 pm2.01 179 . 2 (((¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))) → ¬ (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑)))) → ¬ (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))))
31, 2mt2 190 1 ¬ ((¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))) → ¬ (¬ ((𝜑𝜓) → ¬ (𝜓𝜑)) → ¬ ((𝜑𝜓) → ¬ (𝜓𝜑))))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
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