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Mirrors > Home > ILE Home > Th. List > raltp | Unicode version |
Description: Convert a quantification over a triple to a conjunction. (Contributed by NM, 13-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
raltp.1 | |
raltp.2 | |
raltp.3 | |
raltp.4 | |
raltp.5 | |
raltp.6 |
Ref | Expression |
---|---|
raltp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raltp.1 | . 2 | |
2 | raltp.2 | . 2 | |
3 | raltp.3 | . 2 | |
4 | raltp.4 | . . 3 | |
5 | raltp.5 | . . 3 | |
6 | raltp.6 | . . 3 | |
7 | 4, 5, 6 | raltpg 3423 | . 2 |
8 | 1, 2, 3, 7 | mp3an 1232 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wceq 1243 wcel 1393 wral 2306 cvv 2557 ctp 3377 |
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-3an 887 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-v 2559 df-sbc 2765 df-un 2922 df-sn 3381 df-pr 3382 df-tp 3383 |
This theorem is referenced by: fztpval 8945 |
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