Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frexr | Structured version Visualization version Unicode version |
Description: A function taking real values, is a function taking extended real values. Common case. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
frexr.1 |
Ref | Expression |
---|---|
frexr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frexr.1 | . 2 | |
2 | ressxr 10083 | . . 3 | |
3 | 2 | a1i 11 | . 2 |
4 | 1, 3 | fssd 6057 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wss 3574 wf 5884 cr 9935 cxr 10073 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-f 5892 df-xr 10078 |
This theorem is referenced by: limsupubuz 39945 limsupreuz 39969 limsupvaluz2 39970 supcnvlimsup 39972 limsupgtlem 40009 liminfgelimsupuz 40020 liminflimsupclim 40039 preimaioomnf 40929 incsmf 40951 issmfle 40954 decsmf 40975 |
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