Metamath Proof Explorer

Theorem nfequid

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)

Ref Expression
Assertion nfequid y x = x


Step Hyp Ref Expression
1 equid x = x
2 1 nfth y x = x