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Theorem csbvargi 33091
 Description: The proper substitution of a class for a variable in that variable results in the class (if the class exists), in inference form. (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 3955 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977  Vcvv 3173  ⦋csb 3499 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-v 3175  df-sbc 3403  df-csb 3500 This theorem is referenced by: (None)
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