Theorem zssxr 45641

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 12495	. 2 ⊢ ℤ ⊆ ℝ
2		ressxr 11176	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3943	1 ⊢ ℤ ⊆ ℝ*

Syntax hints:   ⊆ wss 3901  ℝcr 11025  ℝ^*cxr 11165  ℤcz 12488

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-uni 4864  df-br 5099  df-iota 6448  df-fv 6500  df-ov 7361  df-xr 11170  df-neg 11367  df-z 12489

This theorem is referenced by:  limsupequzlem  45966