Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > elunnel1 | Structured version Visualization version Unicode version |
Description: A member of a union that is not member of the first class, is member of the second class. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
elunnel1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elun 3753 | . . 3 | |
2 | 1 | biimpi 206 | . 2 |
3 | 2 | orcanai 952 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 wa 384 wcel 1990 cun 3572 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 |
This theorem is referenced by: fsumsplitsn 14474 fprodsplitsn 14720 founiiun0 39377 infxrpnf 39674 cnrefiisplem 40055 dvnprodlem1 40161 fourierdlem70 40393 fourierdlem71 40394 fourierdlem80 40403 sge0splitmpt 40628 sge0iunmptlemfi 40630 nnfoctbdjlem 40672 hoidmvlelem2 40810 hoidmvlelem3 40811 pimrecltpos 40919 |
Copyright terms: Public domain | W3C validator |