Metamath Proof Explorer


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 → ( 𝜑𝜓 ) )
Assertion spvv ( ∀ 𝑥 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 spvv.1 ( 𝑥 = 𝑦 → ( 𝜑𝜓 ) )
2 1 biimpd ( 𝑥 = 𝑦 → ( 𝜑𝜓 ) )
3 2 spimvw ( ∀ 𝑥 𝜑𝜓 )