Theorem zssxr 45971

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 12586	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11241	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3948	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3907  ℝcr 11087  ℝ^*cxr 11230  ℤcz 12579

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3or 1102  df-3an 1103  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-rab 3418  df-v 3459  df-dif 3910  df-un 3912  df-ss 3924  df-nul 4289  df-if 4484  df-sn 4586  df-pr 4588  df-op 4592  df-uni 4868  df-br 5105  df-iota 6481  df-fv 6533  df-ov 7403  df-xr 11235  df-neg 11432  df-z 12580

This theorem is referenced by:  limsupequzlem  46295