![]() |
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 4684 | . 2 ⊢ (𝐴𝑅𝐵 → 𝐴 ∈ V) |
4 | 1, 3 | mto 663 | 1 ⊢ ¬ 𝐴𝑅𝐵 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 2160 Vcvv 2752 class class class wbr 4018 Rel wrel 4646 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4647 df-rel 4648 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |