Metamath Proof Explorer


Theorem selsALT

Description: Alternate proof of sels , requiring ax-sep but not using el (which is proved from it as elALT ). (especially when the proof of el is inlined in sels ). (Contributed by NM, 4-Jan-2002) Generalize from the proof of elALT . (Revised by BJ, 3-Apr-2019) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion selsALT A V x A x

Proof

Step Hyp Ref Expression
1 snidg A V A A
2 snexg A A A V
3 snidg A A A A
4 eleq2 x = A A x A A
5 2 3 4 spcedv A A x A x
6 1 5 syl A V x A x