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Mirrors > Home > MPE Home > Th. List > vexOLD | Structured version Visualization version GIF version |
Description: Obsolete version of vex 3477 as of 4-Sep-2024. (Contributed by NM, 26-May-1993.) Remove use of ax-12 2171. (Revised by SN, 28-Aug-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
vexOLD | ⊢ 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2015 | . . 3 ⊢ 𝑥 = 𝑥 | |
2 | 1 | vexw 2714 | . 2 ⊢ 𝑥 ∈ {𝑥 ∣ 𝑥 = 𝑥} |
3 | df-v 3475 | . 2 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥} | |
4 | 2, 3 | eleqtrri 2831 | 1 ⊢ 𝑥 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 {cab 2708 Vcvv 3473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1782 df-sb 2068 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 |
This theorem is referenced by: (None) |
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