Theorem expt

Description: Exportation theorem pm3.3 (closed form of ex ) expressed with primitive connectives. (Contributed by NM, 28-Dec-1992)

	Ref	Expression
Assertion	expt	⊢ ( ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm3.2im	⊢ ( 𝜑 → ( 𝜓 → ¬ ( 𝜑 → ¬ 𝜓 ) ) )
2	1	imim1d	⊢ ( 𝜑 → ( ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 ) → ( 𝜓 → 𝜒 ) ) )
3	2	com12	⊢ ( ( ¬ ( 𝜑 → ¬ 𝜓 ) → 𝜒 ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )