Theorem pm2.83

Description: Theorem *2.83 of WhiteheadRussell p. 108. Closed form of syld . (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.83	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → ( 𝜒 → 𝜃 ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim1	⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜒 → 𝜃 ) → ( 𝜓 → 𝜃 ) ) )
2	1	imim3i	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜑 → ( 𝜒 → 𝜃 ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) )