Theorem zssxr 42937

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 12326	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11019	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3930	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3887  ℝcr 10870  ℝ^*cxr 11008  ℤcz 12319

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-iota 6391  df-fv 6441  df-ov 7278  df-xr 11013  df-neg 11208  df-z 12320

This theorem is referenced by:  limsupequzlem  43263