Theorem nbfal 1554

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 1553	. 2 ⊢ ¬ ⊥
2	1	nbn 373	1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))

Syntax hints:  ¬ wn 3   ↔ wb 205  ⊥wfal 1551

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 1542  df-fal 1552

This theorem is referenced by:  nulmo  2714  eq0  4277  ab0  4308  ab0OLD  4309  eq0rdv  4338  rzal  4439  bisym1  34608  wl-1xor  35653  wl-1mintru1  35659  aisfina  44393  aifftbifffaibifff  44417  lindslinindsimp2  45804