Theorem zssxr 45408

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 12620	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11305	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3993	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3951  ℝcr 11154  ℝ^*cxr 11294  ℤcz 12613

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 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3or 1088  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-xr 11299  df-neg 11495  df-z 12614

This theorem is referenced by:  limsupequzlem  45737