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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj105 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj105 | ⊢ 1o ∈ V |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df1o2 8513 | . 2 ⊢ 1o = {∅} | |
| 2 | p0ex 5384 | . 2 ⊢ {∅} ∈ V | |
| 3 | 1, 2 | eqeltri 2837 | 1 ⊢ 1o ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 Vcvv 3480 ∅c0 4333 {csn 4626 1oc1o 8499 |
| 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 ax-sep 5296 ax-nul 5306 ax-pow 5365 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-pw 4602 df-sn 4627 df-suc 6390 df-1o 8506 |
| This theorem is referenced by: bnj106 34882 bnj118 34883 bnj121 34884 bnj125 34886 bnj130 34888 bnj153 34894 |
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