Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rabid2 | Unicode version |
Description: An "identity" law for restricted class abstraction. (Contributed by NM, 9-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
rabid2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abeq2 2146 | . . 3 | |
2 | pm4.71 369 | . . . 4 | |
3 | 2 | albii 1359 | . . 3 |
4 | 1, 3 | bitr4i 176 | . 2 |
5 | df-rab 2315 | . . 3 | |
6 | 5 | eqeq2i 2050 | . 2 |
7 | df-ral 2311 | . 2 | |
8 | 4, 6, 7 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 cab 2026 wral 2306 crab 2310 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-rab 2315 |
This theorem is referenced by: rabxmdc 3249 rabrsndc 3438 class2seteq 3916 dmmptg 4818 fneqeql 5275 fmpt 5319 acexmidlemph 5505 ioomax 8817 iccmax 8818 |
Copyright terms: Public domain | W3C validator |