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Mirrors > Home > MPE Home > Th. List > brabg | Structured version Visualization version Unicode version |
Description: The law of concretion for a binary relation. (Contributed by NM, 16-Aug-1999.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
opelopabg.1 | |
opelopabg.2 | |
brabg.5 |
Ref | Expression |
---|---|
brabg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopabg.1 | . . 3 | |
2 | opelopabg.2 | . . 3 | |
3 | 1, 2 | sylan9bb 736 | . 2 |
4 | brabg.5 | . 2 | |
5 | 3, 4 | brabga 4989 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 class class class wbr 4653 copab 4712 |
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-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-br 4654 df-opab 4713 |
This theorem is referenced by: brab 4998 ideqg 5273 opelcnvg 5302 f1owe 6603 brrpssg 6939 bren 7964 brdomg 7965 brwdom 8472 ltprord 9852 shftfib 13812 efgrelexlema 18162 isref 21312 istrkgld 25358 islnopp 25631 axcontlem5 25848 cmbr 28443 leopg 28981 cvbr 29141 mdbr 29153 dmdbr 29158 soseq 31751 sltval 31800 brsslt 31900 isfne 32334 brabg2 33510 isriscg 33783 lcvbr 34308 |
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