Theorem xchbinxr 302

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

Hypotheses

Ref	Expression
xchbinxr.1	|- (ph <-> -. ps)
xchbinxr.2	|- (ch <-> ps)

Assertion

Ref	Expression
xchbinxr	|- (ph <-> -. ch)

Proof of Theorem xchbinxr

Step	Hyp	Ref	Expression
1		xchbinxr.1	. 2 |- (ph <-> -. ps)
2		xchbinxr.2	. . 3 |- (ch <-> ps)
3	2	bicomi 193	. 2 |- (ps <-> ch)
4	1, 3	xchbinx 301	1 |- (ph <-> -. ch)

Syntax hints:  -. wn 3   <-> wb 176

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 177

This theorem is referenced 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