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Mirrors > Home > ILE Home > Th. List > ssv | GIF version |
Description: Any class is a subclass of the universal class. (Contributed by NM, 31-Oct-1995.) |
Ref | Expression |
---|---|
ssv | ⊢ 𝐴 ⊆ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2741 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ V) | |
2 | 1 | ssriv 3151 | 1 ⊢ 𝐴 ⊆ V |
Colors of variables: wff set class |
Syntax hints: Vcvv 2730 ⊆ wss 3121 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 df-in 3127 df-ss 3134 |
This theorem is referenced by: ddifss 3365 inv1 3451 unv 3452 vss 3462 disj2 3470 pwv 3795 trv 4099 xpss 4719 djussxp 4756 dmv 4827 dmresi 4946 resid 4947 ssrnres 5053 rescnvcnv 5073 cocnvcnv1 5121 relrelss 5137 dffn2 5349 oprabss 5939 ofmres 6115 f1stres 6138 f2ndres 6139 fiintim 6906 djuf1olemr 7031 endjusym 7073 dju1p1e2 7174 suplocexprlemell 7675 seq3val 10414 seqvalcd 10415 seq3-1 10416 seqf 10417 seq3p1 10418 seqf2 10420 seq1cd 10421 seqp1cd 10422 setscom 12456 upxp 13066 uptx 13068 cnmptid 13075 cnmpt1st 13082 cnmpt2nd 13083 |
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