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Mirrors > Home > MPE Home > Th. List > vex | Structured version Visualization version GIF version |
Description: All setvar variables are sets (see isset 3452). Theorem 6.8 of [Quine] p. 43. (Contributed by NM, 26-May-1993.) Remove use of ax-12 2143. (Revised by SN, 28-Aug-2023.) |
Ref | Expression |
---|---|
vex | ⊢ 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2000 | . . 3 ⊢ 𝑥 = 𝑥 | |
2 | 1 | vexw 2783 | . 2 ⊢ 𝑥 ∈ {𝑥 ∣ 𝑥 = 𝑥} |
3 | df-v 3442 | . 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥} | |
4 | 2, 3 | eleqtrri 2884 | 1 ⊢ 𝑥 ∈ V |
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