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Mirrors > Home > ILE Home > Th. List > ralrab2 | Unicode version |
Description: Universal quantification over a restricted class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
ralab2.1 |
Ref | Expression |
---|---|
ralrab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2444 | . . 3 | |
2 | 1 | raleqi 2656 | . 2 |
3 | ralab2.1 | . . 3 | |
4 | 3 | ralab2 2876 | . 2 |
5 | impexp 261 | . . . 4 | |
6 | 5 | albii 1450 | . . 3 |
7 | df-ral 2440 | . . 3 | |
8 | 6, 7 | bitr4i 186 | . 2 |
9 | 2, 4, 8 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wcel 2128 cab 2143 wral 2435 crab 2439 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rab 2444 |
This theorem is referenced by: (None) |
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