Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 2671 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ V) | |
2 | 1 | ssriv 3071 | 1 ⊢ 𝐴 ⊆ V |
Colors of variables: wff set class |
Syntax hints: Vcvv 2660 ⊆ wss 3041 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 df-in 3047 df-ss 3054 |
This theorem is referenced by: ddifss 3284 inv1 3369 unv 3370 vss 3380 disj2 3388 pwv 3705 trv 4008 xpss 4617 djussxp 4654 dmv 4725 dmresi 4844 resid 4845 ssrnres 4951 rescnvcnv 4971 cocnvcnv1 5019 relrelss 5035 dffn2 5244 oprabss 5825 ofmres 6002 f1stres 6025 f2ndres 6026 fiintim 6785 djuf1olemr 6907 endjusym 6949 dju1p1e2 7021 suplocexprlemell 7489 seq3val 10199 seqvalcd 10200 seq3-1 10201 seqf 10202 seq3p1 10203 seqf2 10205 seq1cd 10206 seqp1cd 10207 setscom 11926 upxp 12368 uptx 12370 cnmptid 12377 cnmpt1st 12384 cnmpt2nd 12385 |
Copyright terms: Public domain | W3C validator |