Theorem xchbinxr 679

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 131	. 2 |- ( ps <-> ch )
4	1, 3	xchbinx 678	1 |- ( ph <-> -. ch )

Syntax hints:   -. wn 3   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 610  ax-in2 611

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xordc1  1389  sbnv  1882  ralnex  2459  difab  3397  disjsn  3646  iindif2m  3941  reldm0  4830