Theorem zssxr 45522

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 12484	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11165	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3940	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3898  ℝcr 11014  ℝ^*cxr 11154  ℤcz 12477

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-rab 3397  df-v 3439  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4283  df-if 4477  df-sn 4578  df-pr 4580  df-op 4584  df-uni 4861  df-br 5096  df-iota 6444  df-fv 6496  df-ov 7357  df-xr 11159  df-neg 11356  df-z 12478

This theorem is referenced by:  limsupequzlem  45847