![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > ressxr | GIF version |
Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
ressxr | ⊢ ℝ ⊆ ℝ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3298 | . 2 ⊢ ℝ ⊆ (ℝ ∪ {+∞, -∞}) | |
2 | df-xr 7986 | . 2 ⊢ ℝ* = (ℝ ∪ {+∞, -∞}) | |
3 | 1, 2 | sseqtrri 3190 | 1 ⊢ ℝ ⊆ ℝ* |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3127 ⊆ wss 3129 {cpr 3592 ℝcr 7801 +∞cpnf 7979 -∞cmnf 7980 ℝ*cxr 7981 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-xr 7986 |
This theorem is referenced by: rexpssxrxp 7992 rexr 7993 0xr 7994 rexrd 7997 ltrelxr 8008 iooval2 9902 fzval2 9998 seq3coll 10806 summodclem2a 11373 prodmodclem2a 11568 ismet2 13521 qtopbas 13689 tgqioo 13714 |
Copyright terms: Public domain | W3C validator |