Metamath Proof Explorer


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 } )