Theorem xchnxbir 681

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 132	. 2 ⊢ (𝜑 ↔ 𝜒)
4	1, 3	xchnxbi 680	1 ⊢ (¬ 𝜒 ↔ 𝜓)

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:  3ioran  993  truxortru  1419  truxorfal  1420  falxortru  1421  falxorfal  1422  intirr  5017  sucpw1nel3  7235  hashunlem  10787