Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcsn | GIF version |
Description: The singleton of a setvar is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcsn | ⊢ BOUNDED {𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bdeq 12945 | . . 3 ⊢ BOUNDED 𝑦 = 𝑥 | |
2 | 1 | bdcab 12974 | . 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥} |
3 | df-sn 3503 | . 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥} | |
4 | 2, 3 | bdceqir 12969 | 1 ⊢ BOUNDED {𝑥} |
Colors of variables: wff set class |
Syntax hints: {cab 2103 {csn 3497 BOUNDED wbdc 12965 |
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-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 ax-bd0 12938 ax-bdeq 12945 ax-bdsb 12947 |
This theorem depends on definitions: df-bi 116 df-clab 2104 df-cleq 2110 df-clel 2113 df-sn 3503 df-bdc 12966 |
This theorem is referenced by: bdcpr 12996 bdctp 12997 bdvsn 12999 bdcsuc 13005 |
Copyright terms: Public domain | W3C validator |