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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 637 | . . . . 5 | |
3 | 1, 2 | mpi 15 | . . . 4 |
4 | 3 | alimi 1448 | . . 3 |
5 | df-ral 2453 | . . 3 | |
6 | eq0 3433 | . . 3 | |
7 | 4, 5, 6 | 3imtr4i 200 | . 2 |
8 | rzal 3512 | . 2 | |
9 | 7, 8 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1346 wceq 1348 wcel 2141 wral 2448 c0 3414 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-v 2732 df-dif 3123 df-nul 3415 |
This theorem is referenced by: (None) |
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