Theorem nfequid 2042

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. (Contributed by NM, 13-Jan-2011.) (Revised by NM, 21-Aug-2017.)

Assertion

Ref	Expression
nfequid	⊢ Ⅎ𝑦 𝑥 = 𝑥

Proof of Theorem nfequid

Step	Hyp	Ref	Expression
1		equid 2041	. 2 ⊢ 𝑥 = 𝑥
2	1	nfth 1830	1 ⊢ Ⅎ𝑦 𝑥 = 𝑥

This proof depends on syntax axioms:  Ⅎwnf 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037

This proof depends on definitions:  df-bi 210  df-ex 1809  df-nf 1813

This theorem is used by: (None)