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Theorem nfequid 1678
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
nfequid 𝑦 𝑥 = 𝑥

Proof of Theorem nfequid
StepHypRef Expression
1 equid 1677 . 2 𝑥 = 𝑥
21nfth 1440 1 𝑦 𝑥 = 𝑥
Colors of variables: wff set class
Syntax hints:  wnf 1436
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 1425  ax-ie2 1470  ax-8 1482  ax-17 1506  ax-i9 1510
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by: (None)
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