Theorem a2d

Description: Deduction distributing an embedded antecedent. Deduction form of ax-2 . (Contributed by NM, 23-Jun-1994)

	Ref	Expression
Hypothesis	a2d.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	a2d	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		a2d.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ax-2	⊢ ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) )
3	1 2	syl	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) )