Theorem pm2.86 100

Description: Converse of Axiom ax-2 7. Theorem *2.86 of [WhiteheadRussell] p. 108. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Assertion

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

Proof of Theorem pm2.86

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2	1	pm2.86d 99	1 |- ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  imdi  249