Metamath Proof Explorer


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 ) )