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Mirrors > Home > ILE Home > Th. List > elpwid | Unicode version |
Description: An element of a power class is a subclass. Deduction form of elpwi 3562. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
elpwid.1 |
Ref | Expression |
---|---|
elpwid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwid.1 | . 2 | |
2 | elpwi 3562 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2135 wss 3111 cpw 3553 |
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 2723 df-in 3117 df-ss 3124 df-pw 3555 |
This theorem is referenced by: fopwdom 6793 ssenen 6808 fival 6926 fiuni 6934 3nelsucpw1 7181 elnp1st2nd 7408 ixxssxr 9827 elfzoelz 10072 restid2 12507 epttop 12637 neiss2 12689 blssm 12968 blin2 12979 cncfrss 13109 cncfrss2 13110 pwle2 13719 |
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