Theorem csbvargi 4387

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4386. (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 4386	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

Syntax hints:   = wceq 1541   ∈ wcel 2113  Vcvv 3440  ⦋csb 3849

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-12 2184  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3442  df-sbc 3741  df-csb 3850

This theorem is referenced by:  sbcop  5437  iuninc  32635  f1od2  32798  bnj110  35014  finxpreclem4  37599  brtrclfv2  43968  onfrALTlem4VD  45126  eubrdm  47282