Theorem wl-impchain-mp-2 38157

Description: This theorem is in fact a copy of wl-luk-imtrdi 38139, 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.)

Hypotheses

Ref	Expression
wl-impchain-mp-2.a	⊢ (𝜃 → (𝜒 → 𝜓))
wl-impchain-mp-2.b	⊢ (𝜓 → 𝜑)

Assertion

Ref	Expression
wl-impchain-mp-2	⊢ (𝜃 → (𝜒 → 𝜑))

Proof of Theorem wl-impchain-mp-2

Step	Hyp	Ref	Expression
1		wl-impchain-mp-2.a	. 2 ⊢ (𝜃 → (𝜒 → 𝜓))
2		wl-impchain-mp-2.b	. . 3 ⊢ (𝜓 → 𝜑)
3	2	wl-luk-imim2i 38138	. 2 ⊢ ((𝜒 → 𝜓) → (𝜒 → 𝜑))
4	1, 3	wl-impchain-mp-1 38156	1 ⊢ (𝜃 → (𝜒 → 𝜑))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38126  ax-luk2 38127  ax-luk3 38128

This theorem is used by:  wl-impchain-com-1.4  38162