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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ru | Structured version Visualization version GIF version |
Description: Remove dependency on ax-13 2363 (and df-v 3468) from Russell's paradox ru 3769 expressed with primitive symbols and with a class variable 𝑉. Note the more economical use of elissetv 2806 instead of isset 3479 to avoid use of df-v 3468. (Contributed by BJ, 12-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-ru | ⊢ ¬ {𝑥 ∣ ¬ 𝑥 ∈ 𝑥} ∈ 𝑉 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ru1 36324 | . 2 ⊢ ¬ ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥 ∈ 𝑥} | |
2 | elissetv 2806 | . 2 ⊢ ({𝑥 ∣ ¬ 𝑥 ∈ 𝑥} ∈ 𝑉 → ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥 ∈ 𝑥}) | |
3 | 1, 2 | mto 196 | 1 ⊢ ¬ {𝑥 ∣ ¬ 𝑥 ∈ 𝑥} ∈ 𝑉 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1533 ∃wex 1773 ∈ wcel 2098 {cab 2701 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 |
This theorem is referenced by: (None) |
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