Theorem zssxr 45936

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 12572	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11223	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3945	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3904  ℝcr 11069  ℝ^*cxr 11212  ℤcz 12565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3or 1098  df-3an 1099  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3455  df-dif 3907  df-un 3909  df-ss 3921  df-nul 4286  df-if 4480  df-sn 4582  df-pr 4584  df-op 4588  df-uni 4865  df-br 5100  df-iota 6473  df-fv 6525  df-ov 7395  df-xr 11217  df-neg 11414  df-z 12566

This theorem is referenced by:  limsupequzlem  46260