Theorem xchnxbir 671

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 131	. 2 |- ( ph <-> ch )
4	1, 3	xchnxbi 670	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 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  3ioran  983  truxortru  1409  truxorfal  1410  falxortru  1411  falxorfal  1412  intirr  4990  sucpw1nel3  7189  hashunlem  10717