Theorem csbvargi 4396

Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4395. (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 4395	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2147  Vcvv 3454  ⦋csb 3851

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-12 2216  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-sbc 3743  df-csb 3852

This theorem is used by:  sbcop  5466  f1od2  8145  iuninc  33253  bnj110  35599  finxpreclem4  38585  brtrclfv2  44988  onfrALTlem4VD  46128  eubrdm  48379