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Mirrors > Home > ILE Home > Th. List > vss | Unicode version |
Description: Only the universal class has the universal class as a subclass. (Contributed by NM, 17-Sep-2003.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
vss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3150 | . . 3 | |
2 | 1 | biantrur 301 | . 2 |
3 | eqss 3143 | . 2 | |
4 | 2, 3 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 cvv 2712 wss 3102 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-v 2714 df-in 3108 df-ss 3115 |
This theorem is referenced by: vdif0im 3459 |
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