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Theorem csbvargi 4437
Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4436. (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 4436 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  wcel 2099  Vcvv 3462  csb 3892
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-12 2167  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1537  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2704  df-cleq 2718  df-clel 2803  df-v 3464  df-sbc 3777  df-csb 3893
This theorem is referenced by:  sbcop  5495  iuninc  32481  f1od2  32635  bnj110  34703  finxpreclem4  37101  brtrclfv2  43394  onfrALTlem4VD  44562  eubrdm  46651
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