User blog comment:Fejfo/Uncountable indexed veblen function/@comment-32213734-20180513045616/@comment-32213734-20180514193120

No, I stated the opposite:

sup{β < Γ0 : φβ(β)} = Γ0

but Γ0 ≠ φΓ 0 (Γ0)

Your counter example is also right:

sup{β < ω : φβ(β)} = φ(ω, 0) ≠ φω(ω) = φ(ω, ω)