Metamath Proof Explorer

Theorem ressxr

Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005)

Ref Expression
Assertion ressxr ℝ ⊆ ℝ*

Proof

Step Hyp Ref Expression
1 ssun1 ⊢ ℝ ⊆ ( ℝ ∪ { +∞ , -∞ } )
2 df-xr ⊢ ℝ* = ( ℝ ∪ { +∞ , -∞ } )
3 1 2 sseqtrri ⊢ ℝ ⊆ ℝ*