Theorem icheqid 47466

Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 47456 and icheq 47467 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 47456	1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥

Syntax hints:  [wich 47450

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-ich 47451

This theorem is referenced by: (None)