Theorem bj-csbsn

Description: Substitution in a singleton. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-csbsn	|- [_ A / x ]_ { x } = { A }

Proof

Step	Hyp	Ref	Expression
1		bj-csbsnlem	|- [_ y / x ]_ { x } = { y }
2	1	csbeq2i	|- [_ A / y ]_ [_ y / x ]_ { x } = [_ A / y ]_ { y }
3		csbcow	|- [_ A / y ]_ [_ y / x ]_ { x } = [_ A / x ]_ { x }
4		bj-csbsnlem	|- [_ A / y ]_ { y } = { A }
5	2 3 4	3eqtr3i	|- [_ A / x ]_ { x } = { A }