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	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	impcomd	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		impd.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	com23	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )
3	2	impd	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜓 ) → 𝜃 ) )