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Mirrors > Home > ILE Home > Th. List > pwuni | Unicode version |
Description: A class is a subclass of the power class of its union. Exercise 6(b) of [Enderton] p. 38. (Contributed by NM, 14-Oct-1996.) |
Ref | Expression |
---|---|
pwuni |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elssuni 3811 | . . 3 | |
2 | vex 2724 | . . . 4 | |
3 | 2 | elpw 3559 | . . 3 |
4 | 1, 3 | sylibr 133 | . 2 |
5 | 4 | ssriv 3141 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 wss 3111 cpw 3553 cuni 3783 |
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 df-uni 3784 |
This theorem is referenced by: uniexb 4445 2pwuninelg 6242 istopon 12558 eltg3i 12603 mopnfss 12994 |
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