Theorem xchnxbir 642

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 131	. 2 ⊢ (𝜑 ↔ 𝜒)
4	1, 3	xchnxbi 641	1 ⊢ (¬ 𝜒 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  3ioran  940  truxortru  1356  truxorfal  1357  falxortru  1358  falxorfal  1359  intirr  4833  hashunlem  10275