Theorem imim2 58

Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Its associated inference is imim2i 16. Its associated deduction is imim2d 57. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 6-Sep-2012.)

Assertion

Ref	Expression
imim2	|- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Proof of Theorem imim2

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	imim2d 57	1 |- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  syldd  72  peirceroll  85  imim12  105  pm3.34  610  19.38b  1768  jath  31609  bj-ssbim  32621  19.41rgVD  39138