![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
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 36369 | . 2 ⊢ sngl 𝐵 ⊆ tag 𝐵 | |
2 | 1 | sseli 3973 | 1 ⊢ (𝐴 ∈ sngl 𝐵 → 𝐴 ∈ tag 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2098 sngl bj-csngl 36353 tag bj-ctag 36362 |
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 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-v 3470 df-un 3948 df-in 3950 df-ss 3960 df-bj-tag 36363 |
This theorem is referenced by: bj-sngltag 36371 bj-tagci 36372 |
Copyright terms: Public domain | W3C validator |