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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 3776 | . 2 ⊢ sngl 𝐴 ⊆ (sngl 𝐴 ∪ {∅}) | |
2 | df-bj-tag 32963 | . 2 ⊢ tag 𝐴 = (sngl 𝐴 ∪ {∅}) | |
3 | 1, 2 | sseqtr4i 3638 | 1 ⊢ sngl 𝐴 ⊆ tag 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3572 ⊆ wss 3574 ∅c0 3915 {csn 4177 sngl bj-csngl 32953 tag bj-ctag 32962 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-bj-tag 32963 |
This theorem is referenced by: bj-sngltagi 32970 |
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