MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfequid Structured version   Visualization version   GIF version

Theorem nfequid 2025
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 𝑦 𝑥 = 𝑥

Proof of Theorem nfequid
StepHypRef Expression
1 equid 2024 . 2 𝑥 = 𝑥
21nfth 1808 1 𝑦 𝑥 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wnf 1790
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020
This theorem depends on definitions:  df-bi 210  df-ex 1787  df-nf 1791
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator