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Theorem csbconstgi 34250
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 3695 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑦 = 𝑦)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑦 = 𝑦
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wcel 2145  Vcvv 3351  csb 3682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-sbc 3588  df-csb 3683
This theorem is referenced by:  sbccom2lem  34257
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