Theorem bijust 126

Description: Theorem used to justify definition of biconditional df-bi 128. (The proof was shortened by Josh Purinton, 29-Dec-00.)

Assertion

Ref	Expression
bijust	⊢ ¬ ((φ → φ) → ¬ (φ → φ))

Proof of Theorem bijust

Step	Hyp	Ref	Expression
1		id 9	. 2 ⊢ (φ → φ)
2		pm2.01 80	. 2 ⊢ (((φ → φ) → ¬ (φ → φ)) → ¬ (φ → φ))
3	1, 2	mt2 96	1 ⊢ ¬ ((φ → φ) → ¬ (φ → φ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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