Theorem dnegeq-P4.10 418

Description: Double Negation Equivalence Property.

Assertion

Ref	Expression
dnegeq-P4.10	⊢ (¬ ¬ 𝜑 ↔ 𝜑)

Proof of Theorem dnegeq-P4.10

Step	Hyp	Ref	Expression
1		dnege-P3.30.CL 278	. 2 ⊢ (¬ ¬ 𝜑 → 𝜑)
2		dnegi-P3.29.CL 275	. 2 ⊢ (𝜑 → ¬ ¬ 𝜑)
3	1, 2	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-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by:  negbicancel-P4.11  419  lemma-L4.5  484  allnegex-P5  597  exnegall-P5  598  allasex-P5  599  nfrneg-P6  688  dfexists-P7  959  exnegall-P7  1046  allasex-P7  1048