Metamath Proof Explorer


Theorem snelpwiOLD

Description: Obsolete version of snelpwi as of 17-Jan-2025. (Contributed by NM, 28-May-1995) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion snelpwiOLD
|- ( A e. B -> { A } e. ~P B )

Proof

Step Hyp Ref Expression
1 snssi
 |-  ( A e. B -> { A } C_ B )
2 snex
 |-  { A } e. _V
3 2 elpw
 |-  ( { A } e. ~P B <-> { A } C_ B )
4 1 3 sylibr
 |-  ( A e. B -> { A } e. ~P B )