Theorem pm2.86

Description: Converse of axiom ax-2 . Theorem *2.86 of WhiteheadRussell p. 108. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 3-Apr-2013)

	Ref	Expression
Assertion	pm2.86	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) )
2	1	pm2.86d	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜒 ) ) )