Theorem wl-luk-imtrid

Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. Copy of syl5 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	wl-luk-imtrid.1	|- ( ph -> ps )
	wl-luk-imtrid.2	|- ( ch -> ( ps -> th ) )
Assertion	wl-luk-imtrid	|- ( ch -> ( ph -> th ) )

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imtrid.1	|- ( ph -> ps )
2		wl-luk-imtrid.2	|- ( ch -> ( ps -> th ) )
3	1	wl-luk-imim1i	|- ( ( ps -> th ) -> ( ph -> th ) )
4	2 3	wl-luk-syl	|- ( ch -> ( ph -> th ) )