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Theorem bijust 175
 Description: Theorem used to justify definition of biconditional df-bi 177. (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 19 . 2 (¬ ((φψ) → ¬ (ψφ)) → ¬ ((φψ) → ¬ (ψφ)))
2 pm2.01 160 . 2 (((¬ ((φψ) → ¬ (ψφ)) → ¬ ((φψ) → ¬ (ψφ))) → ¬ (¬ ((φψ) → ¬ (ψφ)) → ¬ ((φψ) → ¬ (ψφ)))) → ¬ (¬ ((φψ) → ¬ (ψφ)) → ¬ ((φψ) → ¬ (ψφ))))
31, 2mt2 170 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-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem is referenced by: (None)
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