Theorem icheqid 43668

Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 43660 and icheq 43669 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 43660	1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥

Syntax hints:  [wich 43654

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2177

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-sb 2070  df-ich 43655

This theorem is referenced by: (None)