Theorem wl-luk-com12

Description: Inference that swaps (commutes) antecedents in an implication. Copy of com12 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	wl-luk-com12.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	wl-luk-com12	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		wl-luk-com12.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		wl-luk-pm2.27	⊢ ( 𝜓 → ( ( 𝜓 → 𝜒 ) → 𝜒 ) )
3	1 2	wl-luk-imtrid	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )