Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nprrel | GIF version |
Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.) |
Ref | Expression |
---|---|
nprrel.1 | ⊢ Rel 𝑅 |
nprrel.2 | ⊢ ¬ 𝐴 ∈ V |
Ref | Expression |
---|---|
nprrel | ⊢ ¬ 𝐴𝑅𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nprrel.2 | . 2 ⊢ ¬ 𝐴 ∈ V | |
2 | nprrel.1 | . . 3 ⊢ Rel 𝑅 | |
3 | 2 | brrelex1i 4629 | . 2 ⊢ (𝐴𝑅𝐵 → 𝐴 ∈ V) |
4 | 1, 3 | mto 652 | 1 ⊢ ¬ 𝐴𝑅𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 2128 Vcvv 2712 class class class wbr 3965 Rel wrel 4591 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-xp 4592 df-rel 4593 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |