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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-abf | Structured version Visualization version GIF version |
Description: Shorter proof of abf 4403 (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-abf.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
bj-abf | ⊢ {𝑥 ∣ 𝜑} = ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ab0 36386 | . 2 ⊢ (∀𝑥 ¬ 𝜑 → {𝑥 ∣ 𝜑} = ∅) | |
2 | bj-abf.1 | . 2 ⊢ ¬ 𝜑 | |
3 | 1, 2 | mpg 1792 | 1 ⊢ {𝑥 ∣ 𝜑} = ∅ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1534 {cab 2705 ∅c0 4323 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-dif 3950 df-nul 4324 |
This theorem is referenced by: (None) |
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