Metamath Proof Explorer


Theorem vtocleg

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 21-Jun-1993)

Ref Expression
Hypothesis vtocleg.1 ⊢ x = A → φ
Assertion vtocleg ⊢ A ∈ V → φ

Proof

Step Hyp Ref Expression
1 vtocleg.1 ⊢ x = A → φ
2 elisset ⊢ A ∈ V → ∃ x x = A
3 1 exlimiv ⊢ ∃ x x = A → φ
4 2 3 syl ⊢ A ∈ V → φ