Theorem wl-impchain-mp-2

Description: This theorem is in fact a copy of wl-luk-imtrdi , and repeated here to demonstrate a recursive proof scheme. The number '2' in the theorem name indicates that a chain of length 2 is modified. (Contributed by Wolf Lammen, 6-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	wl-impchain-mp-2.a	$$⊢\theta \to \left(\chi \to \psi \right)$$
	wl-impchain-mp-2.b	$$⊢\psi \to \phi$$
Assertion	wl-impchain-mp-2	$$⊢\theta \to \left(\chi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-impchain-mp-2.a	$$⊢\theta \to \left(\chi \to \psi \right)$$
2		wl-impchain-mp-2.b	$$⊢\psi \to \phi$$
3	2	wl-luk-imim2i	$$⊢\left(\chi \to \psi \right)\to \left(\chi \to \phi \right)$$
4	1 3	wl-impchain-mp-1	$$⊢\theta \to \left(\chi \to \phi \right)$$