Metamath Proof Explorer


Theorem xchnxbir

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

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

Proof

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