Theorem wl-luk-imim1i 35521

Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. Copy of imim1i 63 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.)

Hypothesis

Ref	Expression
wl-luk-imim1i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
wl-luk-imim1i	⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒))

Proof of Theorem wl-luk-imim1i

Step	Hyp	Ref	Expression
1		wl-luk-imim1i.1	. 2 ⊢ (𝜑 → 𝜓)
2		ax-luk1 35517	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))
3	1, 2	ax-mp 5	1 ⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 35517

This theorem is referenced by:  wl-luk-syl  35522  wl-luk-imtrid  35523