Theorem zssxr 45386

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 12542	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11224	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3958	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3916  ℝcr 11073  ℝ^*cxr 11213  ℤcz 12535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-v 3452  df-dif 3919  df-un 3921  df-ss 3933  df-nul 4299  df-if 4491  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4874  df-br 5110  df-iota 6466  df-fv 6521  df-ov 7392  df-xr 11218  df-neg 11414  df-z 12536

This theorem is referenced by:  limsupequzlem  45713