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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 34804 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ {𝑥} ∈ sngl 𝐴) | |
2 | 1 | abbi2i 2871 | 1 ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∈ wcel 2114 {cab 2716 {csn 4516 sngl bj-csngl 34800 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-11 2162 ax-12 2179 ax-ext 2710 ax-sep 5167 ax-nul 5174 ax-pr 5296 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-tru 1545 df-fal 1555 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-rex 3059 df-v 3400 df-dif 3846 df-un 3848 df-nul 4212 df-sn 4517 df-pr 4519 df-bj-sngl 34801 |
This theorem is referenced by: bj-snglex 34808 bj-taginv 34821 |
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