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Theorem csbvargi 32874
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 3954 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1976  Vcvv 3172  csb 3498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-v 3174  df-sbc 3402  df-csb 3499
This theorem is referenced by: (None)
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