Theorem pm5.501

Description: Theorem *5.501 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.501	|- ( ph -> ( ps <-> ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.1im	|- ( ph -> ( ps -> ( ph <-> ps ) ) )
2		biimp	|- ( ( ph <-> ps ) -> ( ph -> ps ) )
3	2	com12	|- ( ph -> ( ( ph <-> ps ) -> ps ) )
4	1 3	impbid	|- ( ph -> ( ps <-> ( ph <-> ps ) ) )