**Description: **Bound-variable hypothesis
builder for . This theorem tells us
that any variable, including , is effectively not free in
, even though is technically free according to the
traditional definition of free variable. (The proof uses only ax-5 1567,
ax-8 1689, ax-12o 2225, and ax-gen 1556. This shows that this can be proved
without ax9 1956, even though the theorem equid 1690 cannot be. A shorter
proof using ax9 1956 is obtainable from equid 1690 and hbth 1562.) Remark added
2-Dec-2015 NM: This proof does implicitly use ax9v 1669,
which is used for
the derivation of ax12o 2013, unless we consider ax-12o 2225 the starting axiom
rather than ax-12 1953. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |