|   | Mathbox for BJ | < Previous  
      Next > Nearby theorems | |
| 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 4178 | . 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅}) | |
| 2 | df-bj-tag 36976 | . 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅}) | |
| 3 | 1, 2 | sseqtrri 4033 | 1 ⊢ sngl 𝐴 ⊆ tag 𝐴 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∪ cun 3949 ⊆ wss 3951 ∅c0 4333 {csn 4626 sngl bj-csngl 36966 tag bj-ctag 36975 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 df-ss 3968 df-bj-tag 36976 | 
| This theorem is referenced by: bj-sngltagi 36983 | 
| Copyright terms: Public domain | W3C validator |