Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elpwg | Unicode version |
Description: Membership in a power class. Theorem 86 of [Suppes] p. 47. (Contributed by NM, 6-Aug-2000.) |
Ref | Expression |
---|---|
elpwg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2227 | . 2 | |
2 | sseq1 3160 | . 2 | |
3 | vex 2724 | . . 3 | |
4 | 3 | elpw 3559 | . 2 |
5 | 1, 2, 4 | vtoclbg 2782 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 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: elpwi 3562 elpwb 3563 pwidg 3567 prsspwg 3726 elpw2g 4129 snelpwi 4184 prelpwi 4186 pwel 4190 eldifpw 4449 f1opw2 6038 2pwuninelg 6242 tfrlemibfn 6287 tfr1onlembfn 6303 tfrcllembfn 6316 elpmg 6621 fopwdom 6793 fiinopn 12549 ssntr 12669 |
Copyright terms: Public domain | W3C validator |