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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 = 𝐴 → 𝜑 )
Assertion	vtocle	⊢ 𝜑

Proof

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