Theorem spvv

Description: Specialization, using implicit substitution. Version of spv with a disjoint variable condition, which does not require ax-7 , ax-12 , ax-13 . (Contributed by NM, 30-Aug-1993) (Revised by BJ, 31-May-2019)

	Ref	Expression
Hypothesis	spvv.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
Assertion	spvv	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		spvv.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2	1	biimpd	⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
3	2	spimvw	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )