Metamath Proof Explorer


Theorem vtocle

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993) Avoid df-clab . (Revised by Wolf Lammen, 31-May-2025)

Ref Expression
Hypotheses vtocle.1 𝐴 ∈ V
vtocle.2 ( 𝑥 = 𝐴𝜑 )
Assertion vtocle 𝜑

Proof

Step Hyp Ref Expression
1 vtocle.1 𝐴 ∈ V
2 vtocle.2 ( 𝑥 = 𝐴𝜑 )
3 1 isseti 𝑥 𝑥 = 𝐴
4 2 3 exlimiiv 𝜑