![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
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 8415 | . 2 ⊢ 1o = {∅} | |
2 | p0ex 5337 | . 2 ⊢ {∅} ∈ V | |
3 | 1, 2 | eqeltri 2834 | 1 ⊢ 1o ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 Vcvv 3443 ∅c0 4280 {csn 4584 1oc1o 8401 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 ax-sep 5254 ax-nul 5261 ax-pow 5318 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3445 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4281 df-pw 4560 df-sn 4585 df-suc 6321 df-1o 8408 |
This theorem is referenced by: bnj106 33349 bnj118 33350 bnj121 33351 bnj125 33353 bnj130 33355 bnj153 33361 |
Copyright terms: Public domain | W3C validator |