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Theorem nfequid 1631
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 1630 . 2 𝑥 = 𝑥
21nfth 1394 1 𝑦 𝑥 = 𝑥
Colors of variables: wff set class
Syntax hints:  wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379  ax-ie2 1424  ax-8 1436  ax-17 1460  ax-i9 1464
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by: (None)
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