Theorem bisym1

Description: A symmetry with <-> .

See negsym1 for more information. (Contributed by Anthony Hart, 4-Sep-2011)

	Ref	Expression
Assertion	bisym1	|- ( ( ps <-> ( ps <-> F. ) ) -> ( ps <-> ph ) )

Proof

Step	Hyp	Ref	Expression
1		nbfal	|- ( -. ps <-> ( ps <-> F. ) )
2	1	bibi2i	|- ( ( ps <-> -. ps ) <-> ( ps <-> ( ps <-> F. ) ) )
3		pm5.19	|- -. ( ps <-> -. ps )
4	3	pm2.21i	|- ( ( ps <-> -. ps ) -> ( ps <-> ph ) )
5	2 4	sylbir	|- ( ( ps <-> ( ps <-> F. ) ) -> ( ps <-> ph ) )