Theorem nega 78

Description: Double negation. Theorem *2.14 of [WhiteheadRussell] p. 102. (The proof was shortened by David Harvey, 5-Sep-99. An even shorter proof found by Josh Purinton, 29-Dec-00.)

Assertion

Ref	Expression
nega	⊢ (¬ ¬ φ → φ)

Proof of Theorem nega

Step	Hyp	Ref	Expression
1		pm2.21 71	. 2 ⊢ (¬ ¬ φ → (¬ φ → φ))
2		pm2.18 75	. 2 ⊢ ((¬ φ → φ) → φ)
3	1, 2	syl 12	1 ⊢ (¬ ¬ φ → φ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  negb 79  pm2.01 80  con2 82  con2i 89  con3i 90  pm4.13 142  pm2.1 495  indpi 3828

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

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