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Mirrors > Home > MPE Home > Th. List > vexOLD | Structured version Visualization version GIF version |
Description: Obsolete version of vex 3497 as of 28-Aug-2023. All setvar variables are sets (see isset 3506). Theorem 6.8 of [Quine] p. 43. (Contributed by NM, 26-May-1993.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
vexOLD | ⊢ 𝑥 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2019 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | df-v 3496 | . . 3 ⊢ V = {𝑥 ∣ 𝑥 = 𝑥} | |
3 | 2 | abeq2i 2948 | . 2 ⊢ (𝑥 ∈ V ↔ 𝑥 = 𝑥) |
4 | 1, 3 | mpbir 233 | 1 ⊢ 𝑥 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 Vcvv 3494 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-tru 1540 df-ex 1781 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-v 3496 |
This theorem is referenced by: (None) |
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