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Mirrors > Home > ILE Home > Th. List > elpw | Unicode version |
Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
elpw.1 |
Ref | Expression |
---|---|
elpw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpw.1 | . 2 | |
2 | sseq1 3115 | . 2 | |
3 | df-pw 3507 | . 2 | |
4 | 1, 2, 3 | elab2 2827 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 1480 cvv 2681 wss 3066 cpw 3505 |
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-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-v 2683 df-in 3072 df-ss 3079 df-pw 3507 |
This theorem is referenced by: velpw 3512 elpwg 3513 prsspw 3687 pwprss 3727 pwtpss 3728 pwv 3730 sspwuni 3892 iinpw 3898 iunpwss 3899 0elpw 4083 pwuni 4111 snelpw 4130 sspwb 4133 ssextss 4137 pwin 4199 pwunss 4200 iunpw 4396 xpsspw 4646 ssenen 6738 ioof 9747 tgdom 12230 distop 12243 epttop 12248 resttopon 12329 txuni2 12414 |
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