Theorem impbid

Description: Deduce an equivalence from two implications. Deduction associated with impbi and impbii . (Contributed by NM, 24-Jan-1993) Revised to prove it from impbid21d . (Revised by Wolf Lammen, 3-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		impbid.1	|- ( ph -> ( ps -> ch ) )
2		impbid.2	|- ( ph -> ( ch -> ps ) )
3	1 2	impbid21d	|- ( ph -> ( ph -> ( ps <-> ch ) ) )
4	3	pm2.43i	|- ( ph -> ( ps <-> ch ) )