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Mirrors > Home > MPE Home > Th. List > eq0OLDOLD | Structured version Visualization version GIF version |
Description: Obsolete version of eq0 4339 as of 28-Jun-2024. (Contributed by NM, 29-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eq0OLDOLD | ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2892 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | eq0f 4336 | 1 ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∀wal 1531 = wceq 1533 ∈ wcel 2098 ∅c0 4318 |
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-11 2146 ax-12 2166 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1536 df-fal 1546 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-nfc 2877 df-dif 3942 df-nul 4319 |
This theorem is referenced by: (None) |
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