**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 1544,
ax-8 1643, ax-12o 2081, and ax-gen 1533. This shows that this can be proved
without ax9 1889, even though the theorem equid 1644 cannot be. A shorter
proof using ax9 1889 is obtainable from equid 1644 and hbth 1539.) Remark added
2-Dec-2015 NM: This proof does implicitly use ax9v 1636,
which is used for
the derivation of ax12o 1875, unless we consider ax-12o 2081 the starting axiom
rather than ax-12 1866. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |