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Theorem nfequid 1645
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
StepHypRef Expression
1 equid 1644 . 2  |-  x  =  x
21nfth 1540 1  |-  F/ y  x  =  x
Colors of variables: wff set class
Syntax hints:   F/wnf 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-nf 1532
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