Description: Bound-variable hypothesis
builder for 𝑥 = 𝑥. This theorem tells us
that any variable, including 𝑥, is effectively not free in
𝑥 =
𝑥, even though 𝑥 is
technically free according to the
traditional definition of free variable. (The proof uses only ax-4 1728,
ax-7 1922, ax-c9 33193, and ax-gen 1713. This shows that this can be proved
without ax6 2239, even though the theorem equid 1926 cannot be. A shorter
proof using ax6 2239 is obtainable from equid 1926 and hbth 1720.) Remark added
2-Dec-2015 NM: This proof does implicitly use ax6v 1876,
which is used for
the derivation of axc9 2290, unless we consider ax-c9 33193 the starting axiom
rather than ax-13 2234. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |