Theorem xchnxbir 683

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

Hypotheses

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

Assertion

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

Proof of Theorem xchnxbir

Step	Hyp	Ref	Expression
1		xchnxbir.1	. 2 |- ( -. ph <-> ps )
2		xchnxbir.2	. . 3 |- ( ch <-> ph )
3	2	bicomi 132	. 2 |- ( ph <-> ch )
4	1, 3	xchnxbi 682	1 |- ( -. ch <-> ps )

Syntax hints:   -. wn 3   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  3ioran  996  truxortru  1439  truxorfal  1440  falxortru  1441  falxorfal  1442  intirr  5070  sucpw1nel3  7347  hashunlem  10951