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Mirrors > Home > MPE Home > Th. List > ixxval | Structured version Visualization version Unicode version |
Description: Value of the interval function. (Contributed by Mario Carneiro, 3-Nov-2013.) |
Ref | Expression |
---|---|
ixx.1 |
Ref | Expression |
---|---|
ixxval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 4656 | . . . 4 | |
2 | 1 | anbi1d 741 | . . 3 |
3 | 2 | rabbidv 3189 | . 2 |
4 | breq2 4657 | . . . 4 | |
5 | 4 | anbi2d 740 | . . 3 |
6 | 5 | rabbidv 3189 | . 2 |
7 | ixx.1 | . 2 | |
8 | xrex 11829 | . . 3 | |
9 | 8 | rabex 4813 | . 2 |
10 | 3, 6, 7, 9 | ovmpt2 6796 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 crab 2916 class class class wbr 4653 (class class class)co 6650 cmpt2 6652 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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-un 6949 ax-cnex 9992 ax-resscn 9993 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-xr 10078 |
This theorem is referenced by: elixx1 12184 ixxin 12192 iooval 12199 iocval 12212 icoval 12213 iccval 12214 |
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