Theorem 1xr 8030

Description: 1 is an extended real number. (Contributed by Glauco Siliprandi, 2-Jan-2022.)

Assertion

Ref	Expression
1xr	⊢ 1 ∈ ℝ*

Proof of Theorem 1xr

Step	Hyp	Ref	Expression
1		1re 7970	. 2 ⊢ 1 ∈ ℝ
2	1	rexri 8029	1 ⊢ 1 ∈ ℝ*

Syntax hints:   ∈ wcel 2158  1c1 7826  ℝ^*cxr 8005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-1re 7919

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-xr 8010

This theorem is referenced by:  fprodge1  11661