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Mirrors > Home > ILE Home > Th. List > vex | GIF version |
Description: All setvar variables are sets (see isset 2736). Theorem 6.8 of [Quine] p. 43. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
vex | ⊢ 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1694 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | df-v 2732 | . . 3 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥} | |
3 | 2 | abeq2i 2281 | . 2 ⊢ (𝑥 ∈ V ↔ 𝑥 = 𝑥) |
4 | 1, 3 | mpbir 145 | 1 ⊢ 𝑥 ∈ V |
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