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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 34178 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ {𝑥} ∈ sngl 𝐴) | |
2 | 1 | abbi2i 2950 | 1 ⊢ 𝐴 = {𝑥 ∣ {𝑥} ∈ sngl 𝐴} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ∈ wcel 2105 {cab 2796 {csn 4557 sngl bj-csngl 34174 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 ax-sep 5194 ax-nul 5201 ax-pr 5320 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-rex 3141 df-v 3494 df-dif 3936 df-un 3938 df-nul 4289 df-sn 4558 df-pr 4560 df-bj-sngl 34175 |
This theorem is referenced by: bj-snglex 34182 bj-taginv 34195 |
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