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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 / 𝑥𝑥 = 𝐴

Proof of Theorem csbvargi
StepHypRef Expression
1 csbvargi.1 . 2 𝐴 ∈ V
2 csbvarg 4386 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1530  wcel 2107  Vcvv 3499  csb 3886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-12 2169  ax-ext 2797
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2804  df-cleq 2818  df-clel 2897  df-v 3501  df-sbc 3776  df-csb 3887
This theorem is referenced by:  sbcop  5376  iuninc  30229  f1od2  30372  bnj110  32018  finxpreclem4  34546  brtrclfv2  39939  onfrALTlem4VD  41087  eubrdm  43139
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