Theorem icheqid 48134

Description: In an equality for the same setvar variable, the setvar variable is interchangeable by itself. Special case of ichid 48124 and icheq 48135 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 48124	1 ⊢ [𝑥⇄𝑥]𝑥 = 𝑥

Syntax hints:  [wich 48118

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-12 2219

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-sb 2098  df-ich 48119

This theorem is referenced by: (None)