Metamath Proof Explorer


Theorem 0e0icopnf

Description: 0 is a member of ( 0 [,) +oo ) . (Contributed by David A. Wheeler, 8-Dec-2018)

Ref Expression
Assertion 0e0icopnf 0 ∈ ( 0 [,) +∞ )

Proof

Step Hyp Ref Expression
1 0re 0 ∈ ℝ
2 0le0 0 ≤ 0
3 elrege0 ( 0 ∈ ( 0 [,) +∞ ) ↔ ( 0 ∈ ℝ ∧ 0 ≤ 0 ) )
4 1 2 3 mpbir2an 0 ∈ ( 0 [,) +∞ )