Theorem csbconstgf

Description: Substitution doesn't affect a constant B (in which x is not free). (Contributed by NM, 10-Nov-2005)

	Ref	Expression
Hypothesis	csbconstgf.1	⊢ Ⅎ 𝑥 𝐵
Assertion	csbconstgf	⊢ ( 𝐴 ∈ 𝑉 → ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		csbconstgf.1	⊢ Ⅎ 𝑥 𝐵
2		csbtt	⊢ ( ( 𝐴 ∈ 𝑉 ∧ Ⅎ 𝑥 𝐵 ) → ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐵 )
3	1 2	mpan2	⊢ ( 𝐴 ∈ 𝑉 → ⦋ 𝐴 / 𝑥 ⦌ 𝐵 = 𝐵 )