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Mirrors > Home > MPE Home > Th. List > eq0OLDOLD | Structured version Visualization version GIF version |
Description: Obsolete version of eq0 4304 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 2904 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | eq0f 4301 | 1 ⊢ (𝐴 = ∅ ↔ ∀𝑥 ¬ 𝑥 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∀wal 1540 = wceq 1542 ∈ wcel 2107 ∅c0 4283 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-dif 3914 df-nul 4284 |
This theorem is referenced by: (None) |
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