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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 631 | . . . . 5 | |
3 | 1, 2 | mpi 15 | . . . 4 |
4 | 3 | alimi 1431 | . . 3 |
5 | df-ral 2419 | . . 3 | |
6 | eq0 3376 | . . 3 | |
7 | 4, 5, 6 | 3imtr4i 200 | . 2 |
8 | rzal 3455 | . 2 | |
9 | 7, 8 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 wral 2414 c0 3358 |
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 603 ax-in2 604 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 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ne 2307 df-ral 2419 df-v 2683 df-dif 3068 df-nul 3359 |
This theorem is referenced by: (None) |
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