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Mirrors > Home > ILE Home > Th. List > velpw | Unicode version |
Description: Setvar variable membership in a power class (common case). See elpw 3560. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
velpw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2725 | . 2 | |
2 | 1 | elpw 3560 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 2135 wss 3112 cpw 3554 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-in 3118 df-ss 3125 df-pw 3556 |
This theorem is referenced by: ordpwsucss 4539 fabexg 5370 abexssex 6086 qsss 6552 mapval2 6636 pmsspw 6641 uniixp 6679 exmidpw 6866 exmidpweq 6867 pw1fin 6868 pw1dc0el 6869 fival 6927 npsspw 7404 restsspw 12528 istopon 12578 isbasis2g 12610 tgval2 12618 unitg 12629 distop 12652 cldss2 12673 ntreq0 12699 discld 12703 neisspw 12715 restdis 12751 cnntr 12792 |
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