Theorem zssxr 46112

Description: The integers are a subset of the extended reals. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Assertion

Ref	Expression
zssxr	⊢ ℤ ⊆ ℝ*

Proof of Theorem zssxr

Step	Hyp	Ref	Expression
1		zssre 12593	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11248	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3946	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3905  ℝcr 11094  ℝ^*cxr 11237  ℤcz 12586

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1104  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544  df-ov 7413  df-xr 11242  df-neg 11439  df-z 12587

This theorem is referenced by:  limsupequzlem  46436