Theorem xchnxbi 605

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 594	. 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜒)
3		xchnxbi.1	. 2 ⊢ (¬ 𝜑 ↔ 𝜓)
4	2, 3	bitr3i 175	1 ⊢ (¬ 𝜒 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  xchnxbir  606