Theorem notnot1 114

Description: Converse of double negation. Theorem *2.12 of [WhiteheadRussell] p. 101. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)

Assertion

Ref	Expression
notnot1	⊢ (φ → ¬ ¬ φ)

Proof of Theorem notnot1

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (¬ φ → ¬ φ)
2	1	con2i 112	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:  notnoti  115  con1d  116  con4i  122  notnot  282  biortn  395  pm2.13  407  eueq2  3011  ifnot  3701