Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rextpg | Unicode version |
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralprg.1 | |
ralprg.2 | |
raltpg.3 |
Ref | Expression |
---|---|
rextpg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralprg.1 | . . . . . 6 | |
2 | ralprg.2 | . . . . . 6 | |
3 | 1, 2 | rexprg 3611 | . . . . 5 |
4 | 3 | orbi1d 781 | . . . 4 |
5 | raltpg.3 | . . . . . 6 | |
6 | 5 | rexsng 3600 | . . . . 5 |
7 | 6 | orbi2d 780 | . . . 4 |
8 | 4, 7 | sylan9bb 458 | . . 3 |
9 | 8 | 3impa 1177 | . 2 |
10 | df-tp 3568 | . . . 4 | |
11 | 10 | rexeqi 2657 | . . 3 |
12 | rexun 3287 | . . 3 | |
13 | 11, 12 | bitri 183 | . 2 |
14 | df-3or 964 | . 2 | |
15 | 9, 13, 14 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wo 698 w3o 962 w3a 963 wceq 1335 wcel 2128 wrex 2436 cun 3100 csn 3560 cpr 3561 ctp 3562 |
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-3or 964 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-sn 3566 df-pr 3567 df-tp 3568 |
This theorem is referenced by: rextp 3617 |
Copyright terms: Public domain | W3C validator |