Theorem s1dmALT

Description: Alternate version of s1dm , having a shorter proof, but requiring that A is a set. (Contributed by AV, 9-Jan-2020) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	s1dmALT	|- ( A e. S -> dom <" A "> = { 0 } )

Proof

Step	Hyp	Ref	Expression
1		s1val	|- ( A e. S -> <" A "> = { <. 0 , A >. } )
2	1	dmeqd	|- ( A e. S -> dom <" A "> = dom { <. 0 , A >. } )
3		dmsnopg	|- ( A e. S -> dom { <. 0 , A >. } = { 0 } )
4	2 3	eqtrd	|- ( A e. S -> dom <" A "> = { 0 } )