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| Description: One is an element of a nonempty Tarski class. (Contributed by FL, 22-Feb-2011.) | 
| Ref | Expression | 
|---|---|
| tsk1 | ⊢ ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o ∈ 𝑇) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df1o2 8514 | . 2 ⊢ 1o = {∅} | |
| 2 | tsk0 10804 | . . 3 ⊢ ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → ∅ ∈ 𝑇) | |
| 3 | tsksn 10801 | . . 3 ⊢ ((𝑇 ∈ Tarski ∧ ∅ ∈ 𝑇) → {∅} ∈ 𝑇) | |
| 4 | 2, 3 | syldan 591 | . 2 ⊢ ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → {∅} ∈ 𝑇) | 
| 5 | 1, 4 | eqeltrid 2844 | 1 ⊢ ((𝑇 ∈ Tarski ∧ 𝑇 ≠ ∅) → 1o ∈ 𝑇) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 ∈ wcel 2107 ≠ wne 2939 ∅c0 4332 {csn 4625 1oc1o 8500 Tarskictsk 10789 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-10 2140 ax-12 2176 ax-ext 2707 ax-sep 5295 ax-pow 5364 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-nf 1783 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-pw 4601 df-sn 4626 df-pr 4628 df-op 4632 df-br 5143 df-suc 6389 df-1o 8507 df-tsk 10790 | 
| This theorem is referenced by: tsk2 10806 | 
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