Theorem expd

Description: Exportation deduction. (Contributed by NM, 20-Aug-1993) (Proof shortened by Wolf Lammen, 28-Jul-2022)

	Ref	Expression
Hypothesis	expd.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
Assertion	expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		expd.1	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
2	1	expdcom	⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜃 ) ) )
3	2	com3r	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )