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Mirrors > Home > ILE Home > Th. List > ralf0 | Unicode version |
Description: The quantification of a falsehood is vacuous when true. (Contributed by NM, 26-Nov-2005.) |
Ref | Expression |
---|---|
ralf0.1 |
Ref | Expression |
---|---|
ralf0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralf0.1 | . . . . 5 | |
2 | con3 632 | . . . . 5 | |
3 | 1, 2 | mpi 15 | . . . 4 |
4 | 3 | alimi 1435 | . . 3 |
5 | df-ral 2440 | . . 3 | |
6 | eq0 3412 | . . 3 | |
7 | 4, 5, 6 | 3imtr4i 200 | . 2 |
8 | rzal 3491 | . 2 | |
9 | 7, 8 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1333 wceq 1335 wcel 2128 wral 2435 c0 3394 |
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-in1 604 ax-in2 605 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-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-v 2714 df-dif 3104 df-nul 3395 |
This theorem is referenced by: (None) |
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