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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 2566 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ V) | |
2 | 1 | ssriv 2949 | 1 ⊢ 𝐴 ⊆ V |
Colors of variables: wff set class |
Syntax hints: Vcvv 2557 ⊆ wss 2917 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 df-in 2924 df-ss 2931 |
This theorem is referenced by: ddifss 3175 inv1 3253 unv 3254 vss 3264 pssv 3267 disj2 3275 pwv 3579 trv 3866 xpss 4446 djussxp 4481 dmv 4551 dmresi 4661 resid 4662 ssrnres 4763 rescnvcnv 4783 cocnvcnv1 4831 relrelss 4844 dffn2 5047 oprabss 5590 ofmres 5763 f1stres 5786 f2ndres 5787 |
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