Theorem nbfal 1617

Description: The negation of a proposition is equivalent to itself being equivalent to ⊥. (Contributed by Anthony Hart, 14-Aug-2011.)

Assertion

Ref	Expression
nbfal	⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))

Proof of Theorem nbfal

Step	Hyp	Ref	Expression
1		fal 1616	. 2 ⊢ ¬ ⊥
2	1	nbn 364	1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))

Syntax hints:  ¬ wn 3   ↔ wb 198  ⊥wfal 1614

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 199  df-tru 1605  df-fal 1615

This theorem is referenced by:  nulmo  2760  nulmoOLD  2761  zfnuleuOLD  5022  bisym1  33001  aisfina  41974  aifftbifffaibifff  41998  lindslinindsimp2  43249