Theorem xchnxbi 299

Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)

Hypotheses

Ref	Expression
xchnxbi.1	⊢ (¬ φ ↔ ψ)
xchnxbi.2	⊢ (φ ↔ χ)

Assertion

Ref	Expression
xchnxbi	⊢ (¬ χ ↔ ψ)

Proof of Theorem xchnxbi

Step	Hyp	Ref	Expression
1		xchnxbi.2	. . 3 ⊢ (φ ↔ χ)
2	1	notbii 287	. 2 ⊢ (¬ φ ↔ ¬ χ)
3		xchnxbi.1	. 2 ⊢ (¬ φ ↔ ψ)
4	2, 3	bitr3i 242	1 ⊢ (¬ χ ↔ ψ)

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:  xchnxbir  300  ioran  476  pm5.24  864