Theorem xchnxbi 669

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

Hypotheses

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

Assertion

Ref	Expression
xchnxbi	|- ( -. ch <-> ps )

Proof of Theorem xchnxbi

Step	Hyp	Ref	Expression
1		xchnxbi.2	. . 3 |- ( ph <-> ch )
2	1	notbii 657	. 2 |- ( -. ph <-> -. ch )
3		xchnxbi.1	. 2 |- ( -. ph <-> ps )
4	2, 3	bitr3i 185	1 |- ( -. ch <-> ps )

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 603  ax-in2 604

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  xchnxbir  670