Theorem zssxr 45424

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 12595	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11279	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3968	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3926  ℝcr 11128  ℝ^*cxr 11268  ℤcz 12588

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 2707

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 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-ss 3943  df-nul 4309  df-if 4501  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-iota 6484  df-fv 6539  df-ov 7408  df-xr 11273  df-neg 11469  df-z 12589

This theorem is referenced by:  limsupequzlem  45751