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Mirrors > Home > ILE Home > Th. List > iun0 | Unicode version |
Description: An indexed union of the empty set is empty. (Contributed by NM, 26-Mar-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
iun0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3408 | . . . . . 6 | |
2 | 1 | a1i 9 | . . . . 5 |
3 | 2 | nrex 2556 | . . . 4 |
4 | eliun 3864 | . . . 4 | |
5 | 3, 4 | mtbir 661 | . . 3 |
6 | 5, 1 | 2false 691 | . 2 |
7 | 6 | eqriv 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wceq 1342 wcel 2135 wrex 2443 c0 3404 ciun 3860 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-dif 3113 df-nul 3405 df-iun 3862 |
This theorem is referenced by: (None) |
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