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 1810,
ax-7 2015, ax-c9 36028, and ax-gen 1796. This shows that this can be proved
without ax6 2402, even though the theorem equid 2019 cannot be. A shorter
proof using ax6 2402 is obtainable from equid 2019 and hbth 1804.) Remark added
2-Dec-2015 NM: This proof does implicitly use ax6v 1971,
which is used for
the derivation of axc9 2400, unless we consider ax-c9 36028 the starting axiom
rather than ax-13 2390. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |