Theorem zssxr 45848

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 12529	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11187	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3931	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3890  ℝcr 11035  ℝ^*cxr 11176  ℤcz 12522

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3or 1093  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-v 3434  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4269  df-if 4462  df-sn 4563  df-pr 4565  df-op 4569  df-uni 4846  df-br 5080  df-iota 6448  df-fv 6500  df-ov 7366  df-xr 11181  df-neg 11378  df-z 12523

This theorem is referenced by:  limsupequzlem  46172