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Metamath Proof Explorer

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 )