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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 33449 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ {𝑥} ∈ sngl 𝐴) | |
2 | 1 | abbi2i 2915 | 1 ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1653 ∈ wcel 2157 {cab 2785 {csn 4368 sngl bj-csngl 33445 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-13 2377 ax-ext 2777 ax-sep 4975 ax-nul 4983 ax-pr 5097 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-tru 1657 df-ex 1876 df-nf 1880 df-sb 2065 df-clab 2786 df-cleq 2792 df-clel 2795 df-nfc 2930 df-ral 3094 df-rex 3095 df-v 3387 df-dif 3772 df-un 3774 df-nul 4116 df-sn 4369 df-pr 4371 df-bj-sngl 33446 |
This theorem is referenced by: bj-snglex 33453 bj-taginv 33466 |
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