Theorem wl-impchain-mp-1 37384

Description: This theorem is in fact a copy of wl-luk-syl 37359, and repeated here to demonstrate a recursive proof scheme. The number '1' in the theorem name indicates that a chain of length 1 is modified. (Contributed by Wolf Lammen, 6-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-impchain-mp-1.a	⊢ (𝜒 → 𝜓)
wl-impchain-mp-1.b	⊢ (𝜓 → 𝜑)

Assertion

Ref	Expression
wl-impchain-mp-1	⊢ (𝜒 → 𝜑)

Proof of Theorem wl-impchain-mp-1

Step	Hyp	Ref	Expression
1		wl-impchain-mp-1.a	. 2 ⊢ (𝜒 → 𝜓)
2		wl-impchain-mp-1.b	. . 3 ⊢ (𝜓 → 𝜑)
3	2	wl-luk-imim2i 37366	. 2 ⊢ ((𝜒 → 𝜓) → (𝜒 → 𝜑))
4	1, 3	wl-impchain-mp-0 37383	1 ⊢ (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-mp-2  37385  wl-impchain-com-1.3  37389