Metamath Proof Explorer

Theorem eluz2

Description: Membership in an upper set of integers. We use the fact that a function's value (under our function value definition) is empty outside of its domain to show M e. ZZ . (Contributed by NM, 5-Sep-2005) (Revised by Mario Carneiro, 3-Nov-2013)

Ref Expression
Assertion eluz2 N M M N M N


Step Hyp Ref Expression
1 eluzel2 N M M
2 simp1 M N M N M
3 eluz1 M N M N M N
4 ibar M N M N M N M N
5 3 4 bitrd M N M M N M N
6 3anass M N M N M N M N
7 5 6 syl6bbr M N M M N M N
8 1 2 7 pm5.21nii N M M N M N