Theorem notnot2 104

Description: Converse of double negation. Theorem *2.14 of [WhiteheadRussell] p. 102. (Contributed by NM, 5-Aug-1993.) (Proof shortened by David Harvey, 5-Sep-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Assertion

Ref	Expression
notnot2	⊢ (¬ ¬ φ → φ)

Proof of Theorem notnot2

Step	Hyp	Ref	Expression
1		pm2.21 100	. 2 ⊢ (¬ ¬ φ → (¬ φ → φ))
2	1	pm2.18d 103	1 ⊢ (¬ ¬ φ → φ)

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:  notnotrd  105  notnotri  106  con2d  107  con3d  125  notnot  282  condan  769  ecase3ad  911