Theorem icheqid 44913

Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 44903 and icheq 44914 without distinct variables restriction. (Contributed by AV, 29-Jul-2023.)

Assertion

Ref	Expression
icheqid	⊢ [𝑥⇄𝑥]𝑥 = 𝑥

Proof of Theorem icheqid

Step	Hyp	Ref	Expression
1		ichid 44903	1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥

Syntax hints:  [wich 44897

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-sb 2068  df-ich 44898

This theorem is referenced by: (None)