![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > ctex | GIF version |
Description: A class dominated by ω is a set. See also ctfoex 7119 which says that a countable class is a set. (Contributed by Thierry Arnoux, 29-Dec-2016.) (Proof shortened by Jim Kingdon, 13-Mar-2023.) |
Ref | Expression |
---|---|
ctex | ⊢ (𝐴 ≼ ω → 𝐴 ∈ V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reldom 6747 | . 2 ⊢ Rel ≼ | |
2 | 1 | brrelex1i 4671 | 1 ⊢ (𝐴 ≼ ω → 𝐴 ∈ V) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2148 Vcvv 2739 class class class wbr 4005 ωcom 4591 ≼ cdom 6741 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-br 4006 df-opab 4067 df-xp 4634 df-rel 4635 df-dom 6744 |
This theorem is referenced by: cnvct 6811 ssct 6820 xpct 12399 |
Copyright terms: Public domain | W3C validator |