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Mirrors > Home > ILE Home > Th. List > reu7 | Unicode version |
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.) |
Ref | Expression |
---|---|
rmo4.1 |
Ref | Expression |
---|---|
reu7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reu3 2869 | . 2 | |
2 | rmo4.1 | . . . . . . 7 | |
3 | equequ1 1688 | . . . . . . . 8 | |
4 | equcom 1682 | . . . . . . . 8 | |
5 | 3, 4 | syl6bb 195 | . . . . . . 7 |
6 | 2, 5 | imbi12d 233 | . . . . . 6 |
7 | 6 | cbvralv 2652 | . . . . 5 |
8 | 7 | rexbii 2440 | . . . 4 |
9 | equequ1 1688 | . . . . . . 7 | |
10 | 9 | imbi2d 229 | . . . . . 6 |
11 | 10 | ralbidv 2435 | . . . . 5 |
12 | 11 | cbvrexv 2653 | . . . 4 |
13 | 8, 12 | bitri 183 | . . 3 |
14 | 13 | anbi2i 452 | . 2 |
15 | 1, 14 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wral 2414 wrex 2415 wreu 2416 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-reu 2421 df-rmo 2422 |
This theorem is referenced by: (None) |
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