Theorem imim1 76

Description: A closed form of syllogism (see syl 14). Theorem *2.06 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 25-May-2013.)

Assertion

Ref	Expression
imim1	|- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> ch ) ) )

Proof of Theorem imim1

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	imim1d 75	1 |- ( ( ph -> ps ) -> ( ( ps -> ch ) -> ( ph -> 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:  pm2.83  77  pm3.33  343  looinvdc  905  intss  3845