Theorem xchbinx 639

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

Hypotheses

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

Assertion

Ref	Expression
xchbinx	⊢ (𝜑 ↔ ¬ 𝜒)

Proof of Theorem xchbinx

Step	Hyp	Ref	Expression
1		xchbinx.1	. 2 ⊢ (𝜑 ↔ ¬ 𝜓)
2		xchbinx.2	. . 3 ⊢ (𝜓 ↔ 𝜒)
3	2	notbii 626	. 2 ⊢ (¬ 𝜓 ↔ ¬ 𝜒)
4	1, 3	bitri 182	1 ⊢ (𝜑 ↔ ¬ 𝜒)

Syntax hints:  ¬ wn 3   ↔ wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  xchbinxr  640  necon3abii  2281  elirr  4284  en2lp  4297  dm0rn0  4570