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Mirrors > Home > MPE Home > Th. List > el | Structured version Visualization version Unicode version |
Description: Every set is an element of some other set. See elALT 4910 for a shorter proof using more axioms. (Contributed by NM, 4-Jan-2002.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
el |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfpow 4844 | . 2 | |
2 | ax9 2003 | . . . . 5 | |
3 | 2 | alrimiv 1855 | . . . 4 |
4 | ax8 1996 | . . . 4 | |
5 | 3, 4 | embantd 59 | . . 3 |
6 | 5 | spimv 2257 | . 2 |
7 | 1, 6 | eximii 1764 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1481 wex 1704 |
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-8 1992 ax-9 1999 ax-11 2034 ax-12 2047 ax-13 2246 ax-pow 4843 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: dtru 4857 dvdemo2 4903 axpownd 9423 zfcndinf 9440 domep 31698 distel 31709 |
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