Theorem csbvargi 4340

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4339. (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 4339	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

Syntax hints:   = wceq 1538   ∈ wcel 2111  Vcvv 3441  ⦋csb 3828

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-12 2175  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-sbc 3721  df-csb 3829

This theorem is referenced by:  sbcop  5345  iuninc  30324  f1od2  30483  bnj110  32240  finxpreclem4  34811  brtrclfv2  40428  onfrALTlem4VD  41592  eubrdm  43628