Theorem dneg-P1.13a 71

Description: Double Negation Law A.

The other related law is dneg-P1.13b 72.

Assertion

Ref	Expression
dneg-P1.13a	⊢ (¬ ¬ 𝜑 → 𝜑)

Proof of Theorem dneg-P1.13a

Step	Hyp	Ref	Expression
1		poe-P1.11a 65	. 2 ⊢ (¬ ¬ 𝜑 → (¬ 𝜑 → 𝜑))
2		clav-P1.12 68	. 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑)
3	1, 2	syl-P1.2 34	1 ⊢ (¬ ¬ 𝜑 → 𝜑)

Syntax hints:  ¬ wff-neg 9   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem is referenced by:  dneg-P1.13b  72  nclav-P1.14  73  trnsp-P1.15a  76