Theorem vtocleOLD 3556

Description: Obsolete version of vtocle 3555 as of 31-May-2025. (Contributed by NM, 9-Sep-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
vtocle.1	⊢ 𝐴 ∈ V
vtocle.2	⊢ (𝑥 = 𝐴 → 𝜑)

Assertion

Ref	Expression
vtocleOLD	⊢ 𝜑

Distinct variable groups:   𝑥,𝐴   𝜑,𝑥

Proof of Theorem vtocleOLD

Step	Hyp	Ref	Expression
1		vtocle.1	. 2 ⊢ 𝐴 ∈ V
2		vtocle.2	. . 3 ⊢ (𝑥 = 𝐴 → 𝜑)
3	2	vtocleg 3553	. 2 ⊢ (𝐴 ∈ V → 𝜑)
4	1, 3	ax-mp 5	1 ⊢ 𝜑

Syntax hints:   → wi 4   = wceq 1540   ∈ wcel 2108  Vcvv 3480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-clel 2816

This theorem is referenced by: (None)