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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 35159 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ {𝑥} ∈ sngl 𝐴) | |
2 | 1 | abbi2i 2879 | 1 ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 {cab 2715 {csn 4561 sngl bj-csngl 35155 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-11 2154 ax-12 2171 ax-ext 2709 ax-sep 5223 ax-nul 5230 ax-pr 5352 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1542 df-fal 1552 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-rex 3070 df-v 3434 df-dif 3890 df-un 3892 df-nul 4257 df-sn 4562 df-pr 4564 df-bj-sngl 35156 |
This theorem is referenced by: bj-snglex 35163 bj-taginv 35176 |
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