Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > brab2ga | Unicode version |
Description: The law of concretion for a binary relation. See brab2a 4562 for alternate proof. TODO: should one of them be deleted? (Contributed by Mario Carneiro, 28-Apr-2015.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
brab2ga.1 | |
brab2ga.2 |
Ref | Expression |
---|---|
brab2ga |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brab2ga.2 | . . . 4 | |
2 | opabssxp 4583 | . . . 4 | |
3 | 1, 2 | eqsstri 3099 | . . 3 |
4 | 3 | brel 4561 | . 2 |
5 | df-br 3900 | . . . 4 | |
6 | 1 | eleq2i 2184 | . . . 4 |
7 | 5, 6 | bitri 183 | . . 3 |
8 | brab2ga.1 | . . . 4 | |
9 | 8 | opelopab2a 4157 | . . 3 |
10 | 7, 9 | syl5bb 191 | . 2 |
11 | 4, 10 | biadan2 451 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wcel 1465 cop 3500 class class class wbr 3899 copab 3958 cxp 4507 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 |
This theorem is referenced by: reapval 8305 ltxr 9517 |
Copyright terms: Public domain | W3C validator |