Theorem ibib

Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994) (Proof shortened by Wolf Lammen, 24-Jan-2013)

	Ref	Expression
Assertion	ibib	|- ( ( ph -> ps ) <-> ( ph -> ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.501	|- ( ph -> ( ps <-> ( ph <-> ps ) ) )
2	1	pm5.74i	|- ( ( ph -> ps ) <-> ( ph -> ( ph <-> ps ) ) )