Theorem csbvargi 4458

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4457. (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 4457	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

Syntax hints:   = wceq 1537   ∈ wcel 2108  Vcvv 3488  ⦋csb 3921

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-12 2178  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-v 3490  df-sbc 3805  df-csb 3922

This theorem is referenced by:  sbcop  5509  iuninc  32583  f1od2  32735  bnj110  34834  finxpreclem4  37360  brtrclfv2  43689  onfrALTlem4VD  44857  eubrdm  46951