Hilbert Space Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > HSE Home > Th. List > dmdbr | Structured version Visualization version Unicode version |
Description: Binary relation expressing the dual modular pair property. (Contributed by NM, 27-Apr-2006.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dmdbr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2689 | . . . . 5 | |
2 | 1 | anbi1d 741 | . . . 4 |
3 | ineq2 3808 | . . . . . . . 8 | |
4 | 3 | oveq1d 6665 | . . . . . . 7 |
5 | oveq1 6657 | . . . . . . . 8 | |
6 | 5 | ineq2d 3814 | . . . . . . 7 |
7 | 4, 6 | eqeq12d 2637 | . . . . . 6 |
8 | 7 | imbi2d 330 | . . . . 5 |
9 | 8 | ralbidv 2986 | . . . 4 |
10 | 2, 9 | anbi12d 747 | . . 3 |
11 | eleq1 2689 | . . . . 5 | |
12 | 11 | anbi2d 740 | . . . 4 |
13 | sseq1 3626 | . . . . . 6 | |
14 | oveq2 6658 | . . . . . . 7 | |
15 | oveq2 6658 | . . . . . . . 8 | |
16 | 15 | ineq2d 3814 | . . . . . . 7 |
17 | 14, 16 | eqeq12d 2637 | . . . . . 6 |
18 | 13, 17 | imbi12d 334 | . . . . 5 |
19 | 18 | ralbidv 2986 | . . . 4 |
20 | 12, 19 | anbi12d 747 | . . 3 |
21 | df-dmd 29140 | . . 3 | |
22 | 10, 20, 21 | brabg 4994 | . 2 |
23 | 22 | bianabs 924 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 cin 3573 wss 3574 class class class wbr 4653 (class class class)co 6650 cch 27786 chj 27790 cdmd 27824 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-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-iota 5851 df-fv 5896 df-ov 6653 df-dmd 29140 |
This theorem is referenced by: dmdmd 29159 dmdi 29161 dmdbr2 29162 dmdbr3 29164 mddmd2 29168 |
Copyright terms: Public domain | W3C validator |