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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 2379 (and df-v 3443) from Russell's paradox ru 3719 expressed with primitive symbols and with a class variable 𝑉. Note the more economical use of bj-elissetv 34315 instead of isset 3453 to avoid use of df-v 3443. (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 34378 | . 2 ⊢ ¬ ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥 ∈ 𝑥} | |
2 | bj-elissetv 34315 | . 2 ⊢ ({𝑥 ∣ ¬ 𝑥 ∈ 𝑥} ∈ 𝑉 → ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥 ∈ 𝑥}) | |
3 | 1, 2 | mto 200 | 1 ⊢ ¬ {𝑥 ∣ ¬ 𝑥 ∈ 𝑥} ∈ 𝑉 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1538 ∃wex 1781 ∈ wcel 2111 {cab 2776 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 |
This theorem is referenced by: (None) |
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