Theorem zssxr 43281

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 12427	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11120	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3941	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3898  ℝcr 10971  ℝ^*cxr 11109  ℤcz 12420

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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4270  df-if 4474  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4853  df-br 5093  df-iota 6431  df-fv 6487  df-ov 7340  df-xr 11114  df-neg 11309  df-z 12421

This theorem is referenced by:  limsupequzlem  43608