Theorem wl-luk-imim2i

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

	Ref	Expression
Hypothesis	wl-luk-imim2i.1	$$⊢\phi \to \psi$$
Assertion	wl-luk-imim2i	$$⊢\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-imim2i.1	$$⊢\phi \to \psi$$
2		ax-luk1	$$⊢\left(\chi \to \phi \right)\to \left(\left(\phi \to \psi \right)\to \left(\chi \to \psi \right)\right)$$
3	1 2	wl-luk-mpi	$$⊢\left(\chi \to \phi \right)\to \left(\chi \to \psi \right)$$