Theorem pm2.86

Description: Converse of Axiom ax-2 . Theorem *2.86 of WhiteheadRussell p. 108. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 3-Apr-2013)

	Ref	Expression
Assertion	pm2.86	|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2	1	pm2.86d	|- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )