![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 2960 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | df-pw 3353 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | elab2 2684 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-in 2918 df-ss 2925 df-pw 3353 |
This theorem is referenced by: selpw 3358 elpwg 3359 prsspw 3527 pwprss 3567 pwtpss 3568 pwv 3570 sspwuni 3730 iinpw 3733 iunpwss 3734 0elpw 3908 pwuni 3934 snelpw 3940 sspwb 3943 ssextss 3947 pwin 4010 pwunss 4011 iunpw 4177 xpsspw 4393 ioof 8610 |
Copyright terms: Public domain | W3C validator |