Theorem icheqid 48637

Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 48627 and icheq 48638 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 48627	1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥

This proof depends on syntax axioms:  [wich 48621

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2099  df-ich 48622

This theorem is used by: (None)