Theorem dnegeqint-P4.13 423

Description: Double Negative Equivalence Property deducible with intuitionist logic. †

Assertion

Ref	Expression
dnegeqint-P4.13	⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)

Proof of Theorem dnegeqint-P4.13

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. . 3 ⊢ (¬ ¬ ¬ 𝜑 → ¬ ¬ ¬ 𝜑)
2	1	dnegeint-P4.12 421	. 2 ⊢ (¬ ¬ ¬ 𝜑 → ¬ 𝜑)
3		dnegi-P3.29.CL 275	. 2 ⊢ (¬ 𝜑 → ¬ ¬ ¬ 𝜑)
4	2, 3	rcp-NDBII0 239	1 ⊢ (¬ ¬ ¬ 𝜑 ↔ ¬ 𝜑)

Syntax hints:  ¬ wff-neg 9   ↔ wff-bi 104

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

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  negbicancelint-P4.14  424