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Theorem csbconstgi 3849
 Description: The proper substitution of a class for a variable in another variable does not modify it, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.)
Hypothesis
Ref Expression
csbconstgi.1 𝐴 ∈ V
Assertion
Ref Expression
csbconstgi 𝐴 / 𝑥𝑦 = 𝑦
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem csbconstgi
StepHypRef Expression
1 csbconstgi.1 . 2 𝐴 ∈ V
2 csbconstg 3847 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑦 = 𝑦)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑦 = 𝑦
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∈ wcel 2111  Vcvv 3441  ⦋csb 3828 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-sbc 3721  df-csb 3829 This theorem is referenced by:  sbcop  5346  sbccom2lem  35581
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