Theorem nbn3 337

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 115	. 2 ⊢ ¬ ¬ φ
3	2	nbn 336	1 ⊢ (¬ ψ ↔ (ψ ↔ ¬ φ))

Syntax hints:  ¬ wn 3   ↔ wb 176

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 177

This theorem is referenced by: (None)