Theorem zssxr 45844

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 12522	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11180	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3932	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3890  ℝcr 11028  ℝ^*cxr 11169  ℤcz 12515

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6448  df-fv 6500  df-ov 7363  df-xr 11174  df-neg 11371  df-z 12516

This theorem is referenced by:  limsupequzlem  46168