Metamath Proof Explorer


Theorem tsk1

Description: One is an element of a nonempty Tarski class. (Contributed by FL, 22-Feb-2011)

Ref Expression
Assertion tsk1 ⊢ T ∈ Tarski ∧ T ≠ ∅ → 1 𝑜 ∈ T

Proof

Step Hyp Ref Expression
1 df1o2 ⊢ 1 𝑜 = ∅
2 tsk0 ⊢ T ∈ Tarski ∧ T ≠ ∅ → ∅ ∈ T
3 tsksn ⊢ T ∈ Tarski ∧ ∅ ∈ T → ∅ ∈ T
4 2 3 syldan ⊢ T ∈ Tarski ∧ T ≠ ∅ → ∅ ∈ T
5 1 4 eqeltrid ⊢ T ∈ Tarski ∧ T ≠ ∅ → 1 𝑜 ∈ T