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	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	wl-luk-com12	$$⊢\psi \to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		wl-luk-com12.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		wl-luk-pm2.27	$$⊢\psi \to \left(\left(\psi \to \chi \right)\to \chi \right)$$
3	1 2	wl-luk-imtrid	$$⊢\psi \to \left(\phi \to \chi \right)$$