Theorem xchnxbi 332

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 320	. 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜒)
3		xchnxbi.1	. 2 ⊢ (¬ 𝜑 ↔ 𝜓)
4	2, 3	bitr3i 277	1 ⊢ (¬ 𝜒 ↔ 𝜓)

Syntax hints:  ¬ wn 3   ↔ wb 206

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 207

This theorem is referenced by:  xchnxbir  333  ioran  985  pm5.24  1050  2mo  2647  necon1bbii  2989  notabw  4312  psslinpr  11072