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Theorem csbconstgi 3920
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 3918 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑦 = 𝑦)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑦 = 𝑦
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2108  Vcvv 3480  csb 3899
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-sbc 3789  df-csb 3900
This theorem is referenced by:  sbcop  5494  sbccom2lem  38131
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