**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-5 1557,
ax-8 1675, ax-12o 2142, and ax-gen 1546. This shows that this can be proved
without ax9 1949, even though the theorem equid 1676 cannot be. A shorter
proof using ax9 1949 is obtainable from equid 1676 and hbth 1552.) Remark added
2-Dec-2015 NM: This proof does implicitly use ax9v 1655,
which is used for
the derivation of ax12o 1934, unless we consider ax-12o 2142 the starting axiom
rather than ax-12 1925. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |