Theorem csbconstgi 3869

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 3867	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦

Syntax hints:   = wceq 1541   ∈ wcel 2110  Vcvv 3434  ⦋csb 3848

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3436  df-sbc 3740  df-csb 3849

This theorem is referenced by:  sbcop  5427  sbccom2lem  38143