Theorem wl-luk-imim1i

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

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

Proof

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