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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-sngltagi | Structured version Visualization version GIF version |
Description: The singletonization is included in the tagging. (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-sngltagi | ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-snglsstag 36516 | . 2 ⊢ sngl 𝐵 ⊆ tag 𝐵 | |
2 | 1 | sseli 3968 | 1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2098 sngl bj-csngl 36500 tag bj-ctag 36509 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3465 df-un 3945 df-ss 3957 df-bj-tag 36510 |
This theorem is referenced by: bj-sngltag 36518 bj-tagci 36519 |
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