Theorem wl-impchain-mp-2 37385

Description: This theorem is in fact a copy of wl-luk-imtrdi 37367, 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 37366	. 2 ⊢ ((𝜒 → 𝜓) → (𝜒 → 𝜑))
4	1, 3	wl-impchain-mp-1 37384	1 ⊢ (𝜃 → (𝜒 → 𝜑))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 37354  ax-luk2 37355  ax-luk3 37356

This theorem is referenced by:  wl-impchain-com-1.4  37390