![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj923 | 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 |
---|---|
bnj923.1 | ⊢ 𝐷 = (ω ∖ {∅}) |
Ref | Expression |
---|---|
bnj923 | ⊢ (𝑛 ∈ 𝐷 → 𝑛 ∈ ω) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifi 4084 | . 2 ⊢ (𝑛 ∈ (ω ∖ {∅}) → 𝑛 ∈ ω) | |
2 | bnj923.1 | . 2 ⊢ 𝐷 = (ω ∖ {∅}) | |
3 | 1, 2 | eleq2s 2856 | 1 ⊢ (𝑛 ∈ 𝐷 → 𝑛 ∈ ω) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1541 ∈ wcel 2106 ∖ cdif 3905 ∅c0 4280 {csn 4584 ωcom 7798 |
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 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3445 df-dif 3911 |
This theorem is referenced by: bnj1098 33264 bnj544 33375 bnj546 33377 bnj594 33393 bnj580 33394 bnj966 33425 bnj967 33426 bnj970 33428 bnj1001 33440 bnj1053 33457 bnj1071 33458 bnj1118 33465 bnj1128 33471 bnj1145 33474 |
Copyright terms: Public domain | W3C validator |