Theorem csbvargi 4398

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4397. (Contributed by Giovanni Mascellani, 30-May-2019.)

Hypothesis

Ref	Expression
csbvargi.1	⊢ 𝐴 ∈ V

Assertion

Ref	Expression
csbvargi	⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

Proof of Theorem csbvargi

Step	Hyp	Ref	Expression
1		csbvargi.1	. 2 ⊢ 𝐴 ∈ V
2		csbvarg 4397	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

Syntax hints:   = wceq 1567   ∈ wcel 2149  Vcvv 3463  ⦋csb 3861

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-12 2219  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-v 3465  df-sbc 3754  df-csb 3862

This theorem is referenced by:  sbcop  5469  iuninc  32842  f1od2  33001  bnj110  35187  finxpreclem4  37923  brtrclfv2  44338  onfrALTlem4VD  45479  eubrdm  47655