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 1812,
ax-7 2011, ax-c9 36904, and ax-gen 1798. This shows that this can be proved
without ax6 2384, even though Theorem equid 2015 cannot. A shorter proof using
ax6 2384 is obtainable from equid 2015 and hbth 1806.) Remark added 2-Dec-2015
NM: This proof does implicitly use ax6v 1972,
which is used for the
derivation of axc9 2382, unless we consider ax-c9 36904 the starting axiom
rather than ax-13 2372. (Contributed by NM, 13-Jan-2011.) (Revised
by
Mario Carneiro, 12-Oct-2016.) (Proof modification is discouraged.)
(New usage is discouraged.) |