Theorem csbconstgi 3859

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 3857	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦

Syntax hints:   = wceq 1547   ∈ wcel 2119  Vcvv 3432  ⦋csb 3838

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 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-sbc 3731  df-csb 3839

This theorem is referenced by:  sbcop  5436  sbccom2lem  38492