Theorem spsd

Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994)

	Ref	Expression
Hypothesis	spsd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	spsd	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		spsd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		sp	⊢ ( ∀ 𝑥 𝜓 → 𝜓 )
3	2 1	syl5	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 → 𝜒 ) )