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Theorem csbvargi 4381
Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4380. (Contributed by Giovanni Mascellani, 30-May-2019.)
Hypothesis
Ref Expression
csbvargi.1 𝐴 ∈ V
Assertion
Ref Expression
csbvargi 𝐴 / 𝑥𝑥 = 𝐴

Proof of Theorem csbvargi
StepHypRef Expression
1 csbvargi.1 . 2 𝐴 ∈ V
2 csbvarg 4380 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  wcel 2105  Vcvv 3492  csb 3880
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-v 3494  df-sbc 3770  df-csb 3881
This theorem is referenced by:  sbcop  5371  iuninc  30240  f1od2  30383  bnj110  32029  finxpreclem4  34557  brtrclfv2  39950  onfrALTlem4VD  41097  eubrdm  43148
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