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 / 𝑥⦌𝑦 = 𝑦

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem csbconstgi

Step	Hyp	Ref	Expression
1		csbconstgi.1	. 2 ⊢ 𝐴 ∈ V
2		csbconstg 3918	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦

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