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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-snglsstag | Structured version Visualization version GIF version |
Description: The singletonization is included in the tagging. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-snglsstag | ⊢ sngl 𝐴 ⊆ tag 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 4062 | . 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅}) | |
2 | df-bj-tag 34808 | . 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅}) | |
3 | 1, 2 | sseqtrri 3914 | 1 ⊢ sngl 𝐴 ⊆ tag 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3841 ⊆ wss 3843 ∅c0 4211 {csn 4516 sngl bj-csngl 34798 tag bj-ctag 34807 |
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-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-v 3400 df-un 3848 df-in 3850 df-ss 3860 df-bj-tag 34808 |
This theorem is referenced by: bj-sngltagi 34815 |
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