Theorem nbn3 700

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 645	. 2 ⊢ ¬ ¬ 𝜑
3	2	nbn 699	1 ⊢ (¬ 𝜓 ↔ (𝜓 ↔ ¬ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)