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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-2ex | Structured version Visualization version GIF version |
Description: 2𝑜 is a set. (Contributed by BJ, 6-Apr-2019.) |
Ref | Expression |
---|---|
bj-2ex | ⊢ 2𝑜 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2o 7722 | . 2 ⊢ 2𝑜 = suc 1𝑜 | |
2 | bj-1ex 33236 | . . 3 ⊢ 1𝑜 ∈ V | |
3 | 2 | sucex 7168 | . 2 ⊢ suc 1𝑜 ∈ V |
4 | 1, 3 | eqeltri 2827 | 1 ⊢ 2𝑜 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2131 Vcvv 3332 suc csuc 5878 1𝑜c1o 7714 2𝑜c2o 7715 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1863 ax-4 1878 ax-5 1980 ax-6 2046 ax-7 2082 ax-8 2133 ax-9 2140 ax-10 2160 ax-11 2175 ax-12 2188 ax-13 2383 ax-ext 2732 ax-sep 4925 ax-nul 4933 ax-pr 5047 ax-un 7106 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1627 df-ex 1846 df-nf 1851 df-sb 2039 df-clab 2739 df-cleq 2745 df-clel 2748 df-nfc 2883 df-rex 3048 df-v 3334 df-dif 3710 df-un 3712 df-in 3714 df-ss 3721 df-nul 4051 df-sn 4314 df-pr 4316 df-uni 4581 df-suc 5882 df-1o 7721 df-2o 7722 |
This theorem is referenced by: (None) |
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