![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-snglinv | Structured version Visualization version GIF version |
Description: Inverse of singletonization. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-snglinv | ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-snglc 32150 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ {𝑥} ∈ sngl 𝐴) | |
2 | 1 | abbi2i 2725 | 1 ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∈ wcel 1977 {cab 2596 {csn 4125 sngl bj-csngl 32146 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 df-rex 2902 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 df-sn 4126 df-pr 4128 df-bj-sngl 32147 |
This theorem is referenced by: bj-snglex 32154 bj-taginv 32167 |
Copyright terms: Public domain | W3C validator |