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Mirrors > Home > MPE Home > Th. List > pwid | Structured version Visualization version Unicode version |
Description: A set is a member of its power class. Theorem 87 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
pwid.1 |
Ref | Expression |
---|---|
pwid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pwid.1 | . 2 | |
2 | pwidg 4173 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cvv 3200 cpw 4158 |
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-in 3581 df-ss 3588 df-pw 4160 |
This theorem is referenced by: pwnex 6968 r1ordg 8641 rankr1id 8725 cfss 9087 0ram 15724 evl1fval1lem 19694 bastg 20770 fincmp 21196 restlly 21286 ptbasfi 21384 zfbas 21700 ustfilxp 22016 metustfbas 22362 minveclem3b 23199 wilthlem3 24796 coinflipprob 30541 mapdunirnN 36939 pwtrrVD 39060 vsetrec 42446 |
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