Theorem zssxr 45346

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 12617	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11302	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 4004	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3962  ℝcr 11151  ℝ^*cxr 11291  ℤcz 12610

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-iota 6515  df-fv 6570  df-ov 7433  df-xr 11296  df-neg 11492  df-z 12611

This theorem is referenced by:  limsupequzlem  45677