Theorem imim2 49

Description: A closed form of syllogism (see syl 14). Theorem *2.05 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (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 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	imim2d 48	1 |- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Syntax hints:   -> wi 4

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

This theorem is referenced by:  syldd  61  pm3.34  328  spimth  1623  spsbim  1724  elabgft1  9917  bj-rspgt  9925  bj-findis  10104