Theorem wl-luk-a1d 35518

Description: Deduction introducing an embedded antecedent. Copy of imim2 58 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-luk-a1d.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
wl-luk-a1d	⊢ (𝜑 → (𝜒 → 𝜓))

Proof of Theorem wl-luk-a1d

Step	Hyp	Ref	Expression
1		wl-luk-a1d.1	. 2 ⊢ (𝜑 → 𝜓)
2		wl-luk-ax1 35511	. 2 ⊢ (𝜓 → (𝜒 → 𝜓))
3	1, 2	wl-luk-syl 35501	1 ⊢ (𝜑 → (𝜒 → 𝜓))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 35496  ax-luk2 35497  ax-luk3 35498

This theorem is referenced by:  wl-luk-ax2  35519