Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elpwid | Unicode version |
Description: An element of a power class is a subclass. Deduction form of elpwi 3519. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
elpwid.1 |
Ref | Expression |
---|---|
elpwid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpwid.1 | . 2 | |
2 | elpwi 3519 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 wss 3071 cpw 3510 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-pw 3512 |
This theorem is referenced by: fopwdom 6730 ssenen 6745 fival 6858 fiuni 6866 elnp1st2nd 7284 ixxssxr 9683 elfzoelz 9924 restid2 12129 epttop 12259 neiss2 12311 blssm 12590 blin2 12601 cncfrss 12731 cncfrss2 12732 pwle2 13193 |
Copyright terms: Public domain | W3C validator |