Theorem iunxsn

Description: A singleton index picks out an instance of an indexed union's argument. (Contributed by NM, 26-Mar-2004) (Proof shortened by Mario Carneiro, 25-Jun-2016)

	Ref	Expression
Hypotheses	iunxsn.1	|- A e. _V
	iunxsn.2	|- ( x = A -> B = C )
Assertion	iunxsn	|- U_ x e. { A } B = C

Proof

Step	Hyp	Ref	Expression
1		iunxsn.1	|- A e. _V
2		iunxsn.2	|- ( x = A -> B = C )
3	2	iunxsng	|- ( A e. _V -> U_ x e. { A } B = C )
4	1 3	ax-mp	|- U_ x e. { A } B = C