Theorem nbfal 1557

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 1556	. 2 ⊢ ¬ ⊥
2	1	nbn 373	1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))

Syntax hints:  ¬ wn 3   ↔ wb 205  ⊥wfal 1554

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 206  df-tru 1545  df-fal 1555

This theorem is referenced by:  nulmo  2709  eq0  4344  ab0  4375  ab0OLD  4376  eq0rdv  4405  rzal  4509  bisym1  35304  wl-1xor  36363  wl-1mintru1  36369  aisfina  45608  aifftbifffaibifff  45632  lindslinindsimp2  47144