Theorem vtocle 2929

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)

Hypotheses

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

Assertion

Ref	Expression
vtocle	⊢ φ

Distinct variable groups:   x,A   φ,x

Proof of Theorem vtocle

Step	Hyp	Ref	Expression
1		vtocle.1	. 2 ⊢ A ∈ V
2		vtocle.2	. . 3 ⊢ (x = A → φ)
3	2	vtocleg 2926	. 2 ⊢ (A ∈ V → φ)
4	1, 3	ax-mp 5	1 ⊢ φ

Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  Vcvv 2860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2862

This theorem is referenced by: (None)