Theorem wl-impchain-mp-1 38292

Description: This theorem is in fact a copy of wl-luk-syl 38267, 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 38274	. 2 ⊢ ((𝜒 → 𝜓) → (𝜒 → 𝜑))
4	1, 3	wl-impchain-mp-0 38291	1 ⊢ (𝜒 → 𝜑)

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-luk1 38262  ax-luk2 38263  ax-luk3 38264

This theorem is used by:  wl-impchain-mp-2  38293  wl-impchain-com-1.3  38297