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Mirrors > Home > ILE Home > Th. List > ral0 | Unicode version |
Description: Vacuous universal quantification is always true. (Contributed by NM, 20-Oct-2005.) |
Ref | Expression |
---|---|
ral0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3362 | . . 3 | |
2 | 1 | pm2.21i 635 | . 2 |
3 | 2 | rgen 2483 | 1 |
Colors of variables: wff set class |
Syntax hints: 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-ral 2419 df-v 2683 df-dif 3068 df-nul 3359 |
This theorem is referenced by: 0iin 3866 po0 4228 so0 4243 we0 4278 ord0 4308 omsinds 4530 mpt0 5245 iso0 5711 ixp0x 6613 ac6sfi 6785 fimax2gtri 6788 finomni 7005 uzsinds 10208 seq3f1olemp 10268 rexfiuz 10754 fimaxre2 10991 2prm 11797 bj-nntrans 13138 |
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