Theorem xchbinxr 641

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

Hypotheses

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

Assertion

Ref	Expression
xchbinxr	⊢ (𝜑 ↔ ¬ 𝜒)

Proof of Theorem xchbinxr

Step	Hyp	Ref	Expression
1		xchbinxr.1	. 2 ⊢ (𝜑 ↔ ¬ 𝜓)
2		xchbinxr.2	. . 3 ⊢ (𝜒 ↔ 𝜓)
3	2	bicomi 130	. 2 ⊢ (𝜓 ↔ 𝜒)
4	1, 3	xchbinx 640	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 577  ax-in2 578

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  xordc1  1325  sbnv  1811  ralnex  2363  difab  3249  disjsn  3472  iindif2m  3765  reldm0  4601