Theorem xchnxbir 300

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

Hypotheses

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

Assertion

Ref	Expression
xchnxbir	⊢ (¬ χ ↔ ψ)

Proof of Theorem xchnxbir

Step	Hyp	Ref	Expression
1		xchnxbir.1	. 2 ⊢ (¬ φ ↔ ψ)
2		xchnxbir.2	. . 3 ⊢ (χ ↔ φ)
3	2	bicomi 193	. 2 ⊢ (φ ↔ χ)
4	1, 3	xchnxbi 299	1 ⊢ (¬ χ ↔ ψ)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  3ioran  950  nsspssun  3489  undif3  3516