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Mirrors > Home > ILE Home > Th. List > reusv3i | Unicode version |
Description: Two ways of expressing existential uniqueness via an indirect equality. (Contributed by NM, 23-Dec-2012.) |
Ref | Expression |
---|---|
reusv3.1 | |
reusv3.2 |
Ref | Expression |
---|---|
reusv3i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reusv3.1 | . . . . . 6 | |
2 | reusv3.2 | . . . . . . 7 | |
3 | 2 | eqeq2d 2151 | . . . . . 6 |
4 | 1, 3 | imbi12d 233 | . . . . 5 |
5 | 4 | cbvralv 2654 | . . . 4 |
6 | 5 | biimpi 119 | . . 3 |
7 | raaanv 3470 | . . . 4 | |
8 | anim12 341 | . . . . . . 7 | |
9 | eqtr2 2158 | . . . . . . 7 | |
10 | 8, 9 | syl6 33 | . . . . . 6 |
11 | 10 | ralimi 2495 | . . . . 5 |
12 | 11 | ralimi 2495 | . . . 4 |
13 | 7, 12 | sylbir 134 | . . 3 |
14 | 6, 13 | mpdan 417 | . 2 |
15 | 14 | rexlimivw 2545 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wral 2416 wrex 2417 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 |
This theorem is referenced by: reusv3 4381 |
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