Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opelopabsbALT | Unicode version |
Description: The law of concretion in terms of substitutions. Less general than opelopabsb 4152, but having a much shorter proof. (Contributed by NM, 30-Sep-2002.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
opelopabsbALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1627 | . . 3 | |
2 | vex 2663 | . . . . . . 7 | |
3 | vex 2663 | . . . . . . 7 | |
4 | 2, 3 | opth 4129 | . . . . . 6 |
5 | equcom 1667 | . . . . . . 7 | |
6 | equcom 1667 | . . . . . . 7 | |
7 | 5, 6 | anbi12ci 456 | . . . . . 6 |
8 | 4, 7 | bitri 183 | . . . . 5 |
9 | 8 | anbi1i 453 | . . . 4 |
10 | 9 | 2exbii 1570 | . . 3 |
11 | 1, 10 | bitri 183 | . 2 |
12 | elopab 4150 | . 2 | |
13 | 2sb5 1936 | . 2 | |
14 | 11, 12, 13 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 wsb 1720 cop 3500 copab 3958 |
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-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 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-opab 3960 |
This theorem is referenced by: inopab 4641 cnvopab 4910 |
Copyright terms: Public domain | W3C validator |