Theorem nbfal 1325

Description: If something is not true, it outputs ⊥. (Contributed by Anthony Hart, 14-Aug-2011.)

Assertion

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

Proof of Theorem nbfal

Step	Hyp	Ref	Expression
1		fal 1322	. 2 ⊢ ¬ ⊥
2	1	nbn 336	1 ⊢ (¬ φ ↔ (φ ↔ ⊥ ))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176   ⊥ wfal 1317

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-tru 1319  df-fal 1320

This theorem is used by: (None)