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Theorem csbvargi 4319
Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4318. (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 4318 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑥 = 𝐴)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑥 = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  wcel 2113  Vcvv 3397  csb 3788
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1916  ax-6 1974  ax-7 2019  ax-8 2115  ax-9 2123  ax-12 2178  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3399  df-sbc 3680  df-csb 3789
This theorem is referenced by:  sbcop  5343  iuninc  30466  f1od2  30623  bnj110  32401  finxpreclem4  35177  brtrclfv2  40865  onfrALTlem4VD  42028  eubrdm  44053
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