Theorem snopsuppss

Description: The support of a singleton containing an ordered pair is a subset of the singleton containing the first element of the ordered pair, i.e. it is empty or the singleton itself. (Contributed by AV, 19-Jul-2019)

	Ref	Expression
Assertion	snopsuppss	|- ( { <. X , Y >. } supp Z ) C_ { X }

Proof

Step	Hyp	Ref	Expression
1		suppssdm	|- ( { <. X , Y >. } supp Z ) C_ dom { <. X , Y >. }
2		dmsnopss	|- dom { <. X , Y >. } C_ { X }
3	1 2	sstri	|- ( { <. X , Y >. } supp Z ) C_ { X }