Theorem xchnxbir 300

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 193	. 2 |- (ph <-> ch)
4	1, 3	xchnxbi 299	1 |- (-. ch <-> ps)

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:  3ioran  950  nsspssun  3489  undif3  3516