Theorem nbn3 690

Description: Transfer falsehood via equivalence. (Contributed by NM, 11-Sep-2006.)

Hypothesis

Ref	Expression
nbn3.1	⊢ 𝜑

Assertion

Ref	Expression
nbn3	⊢ (¬ 𝜓 ↔ (𝜓 ↔ ¬ 𝜑))

Proof of Theorem nbn3

Step	Hyp	Ref	Expression
1		nbn3.1	. . 3 ⊢ 𝜑
2	1	notnoti 635	. 2 ⊢ ¬ ¬ 𝜑
3	2	nbn 689	1 ⊢ (¬ 𝜓 ↔ (𝜓 ↔ ¬ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)