Theorem nfequid 1690

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	|- F/ y x = x

Proof of Theorem nfequid

Step	Hyp	Ref	Expression
1		equid 1689	. 2 |- x = x
2	1	nfth 1452	1 |- F/ y x = x

Syntax hints:   F/wnf 1448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1437  ax-ie2 1482  ax-8 1492  ax-17 1514  ax-i9 1518

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by: (None)