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	⊢ ( 𝜃 → ( 𝜒 → 𝜓 ) )
	wl-impchain-mp-2.b	⊢ ( 𝜓 → 𝜑 )
Assertion	wl-impchain-mp-2	⊢ ( 𝜃 → ( 𝜒 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		wl-impchain-mp-2.a	⊢ ( 𝜃 → ( 𝜒 → 𝜓 ) )
2		wl-impchain-mp-2.b	⊢ ( 𝜓 → 𝜑 )
3	2	wl-luk-imim2i	⊢ ( ( 𝜒 → 𝜓 ) → ( 𝜒 → 𝜑 ) )
4	1 3	wl-impchain-mp-1	⊢ ( 𝜃 → ( 𝜒 → 𝜑 ) )