Theorem nbfal 1553

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 1552	. 2 ⊢ ¬ ⊥
2	1	nbn 376	1 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))

Syntax hints:  ¬ wn 3   ↔ wb 209  ⊥wfal 1550

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 210  df-tru 1541  df-fal 1551

This theorem is referenced by:  nulmo  2734  eq0  4242  ab0  4272  eq0rdv  4300  rzal  4401  bisym1  34157  wl-1xor  35179  wl-1mintru1  35185  aisfina  43857  aifftbifffaibifff  43881  lindslinindsimp2  45237