Theorem nbn3 725

Description: Transfer falsehood via equivalence.

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	negbi 87	. 2 ⊢ ¬ ¬ φ
3	2	nbn 724	1 ⊢ (¬ ψ ↔ (ψ ↔ ¬ φ))

Syntax hints:  ¬ wn 2   ↔ wb 146

This theorem is referenced by:  zfnuleu 2712

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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