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Mirrors > Home > ILE Home > Th. List > r19.12sn | Unicode version |
Description: Special case of r19.12 2422 where its converse holds. (Contributed by NM, 19-May-2008.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
r19.12sn.1 |
Ref | Expression |
---|---|
r19.12sn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.12sn.1 | . 2 | |
2 | sbcralg 2836 | . . 3 | |
3 | rexsnsOLD 3410 | . . 3 | |
4 | rexsnsOLD 3410 | . . . 4 | |
5 | 4 | ralbidv 2326 | . . 3 |
6 | 2, 3, 5 | 3bitr4d 209 | . 2 |
7 | 1, 6 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 98 wcel 1393 wral 2306 wrex 2307 cvv 2557 wsbc 2764 csn 3375 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-sn 3381 |
This theorem is referenced by: (None) |
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