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Mirrors > Home > MPE Home > Th. List > n0 | Structured version Visualization version GIF version |
Description: A class is nonempty if and only if it has at least one element. Proposition 5.17(1) of [TakeutiZaring] p. 20. (Contributed by NM, 29-Sep-2006.) |
Ref | Expression |
---|---|
n0 | ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2951 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | n0f 4233 | 1 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) |
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