Theorem csbconstgi 3876

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 3874	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦

Syntax hints:   = wceq 1563   ∈ wcel 2145  Vcvv 3457  ⦋csb 3855

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459  df-sbc 3748  df-csb 3856

This theorem is referenced by:  sbcop  5462  sbccom2lem  38635