Theorem xchbinxr 302

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 193	. 2 ⊢ (ψ ↔ χ)
4	1, 3	xchbinx 301	1 ⊢ (φ ↔ ¬ χ)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by:  3anor  948  nanbi  1294  2nalexn  1573  ralnex  2625  rexnal  2626  nss  3330  difdif  3393  difab  3524  ssdif0  3610  difin0ss  3617  disjsn  3787  iundif2  4034  iindif2  4036  tfinsuc  4499