Theorem wl-imim2i 33253

Description: Inference adding common antecedents in an implication. Copy of imim2i 16 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-imim2i.1	|- ( ph -> ps )

Assertion

Ref	Expression
wl-imim2i	|- ( ( ch -> ph ) -> ( ch -> ps ) )

Proof of Theorem wl-imim2i

Step	Hyp	Ref	Expression
1		wl-imim2i.1	. 2 |- ( ph -> ps )
2		ax-luk1 33241	. 2 |- ( ( ch -> ph ) -> ( ( ph -> ps ) -> ( ch -> ps ) ) )
3	1, 2	wl-mpi 33252	1 |- ( ( 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-syl6  33254  wl-ja  33261  wl-impchain-mp-1  33271  wl-impchain-mp-2  33272