Theorem wl-imim2 33262

Description: A closed form of syllogism (see syl 17). Theorem *2.05 of [WhiteheadRussell] p. 100. Copy of imim2 58 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem wl-imim2

Step	Hyp	Ref	Expression
1		ax-luk1 33241	. 2 |- ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) )
2	1	wl-com12 33258	1 |- ( ( ph -> ps ) -> ( ( ch -> ph ) -> ( ch -> ps ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-ax2  33264