Theorem bibi1i

Description: Inference adding a biconditional to the right in an equivalence. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	bibi2i.1	|- ( ph <-> ps )
Assertion	bibi1i	|- ( ( ph <-> ch ) <-> ( ps <-> ch ) )

Proof

Step	Hyp	Ref	Expression
1		bibi2i.1	|- ( ph <-> ps )
2		bicom	|- ( ( ph <-> ch ) <-> ( ch <-> ph ) )
3	1	bibi2i	|- ( ( ch <-> ph ) <-> ( ch <-> ps ) )
4		bicom	|- ( ( ch <-> ps ) <-> ( ps <-> ch ) )
5	2 3 4	3bitri	|- ( ( ph <-> ch ) <-> ( ps <-> ch ) )