Theorem pm4.13 142

Description: Double negation. Theorem *4.13 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
pm4.13	⊢ (φ ↔ ¬ ¬ φ)

Proof of Theorem pm4.13

Step	Hyp	Ref	Expression
1		negb 79	. 2 ⊢ (φ → ¬ ¬ φ)
2		nega 78	. 2 ⊢ (¬ ¬ φ → φ)
3	1, 2	impbi 139	1 ⊢ (φ ↔ ¬ ¬ φ)

Syntax hints:  ¬ wn 1   ↔ wb 127

This theorem is referenced by:  imor 204  iman 205  ianor 253  ioran 254  oran 255  xor 500  alex 717  sbn2 881  symdif2 1690  chrelat2 5758

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

This theorem depends on definitions:  df-bi 128

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