Theorem impcomd

Description: Importation deduction with commuted antecedents. (Contributed by Peter Mazsa, 24-Sep-2022) (Proof shortened by Wolf Lammen, 22-Oct-2022)

	Ref	Expression
Hypothesis	impd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	impcomd	$$⊢\phi \to \left(\left(\chi \wedge \psi \right)\to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		impd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2	1	com23	$$⊢\phi \to \left(\chi \to \left(\psi \to \theta \right)\right)$$
3	2	impd	$$⊢\phi \to \left(\left(\chi \wedge \psi \right)\to \theta \right)$$