Theorem csbconstgi 3873

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 3871	. 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦)
3	1, 2	ax-mp 5	1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦

This proof depends on syntax axioms:   = wceq 1569   ∈ wcel 2142  Vcvv 3454  ⦋csb 3852

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-sbc 3744  df-csb 3853

This theorem is used by:  sbcop  5470  sbccom2lem  38801