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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-abf | Structured version Visualization version GIF version |
Description: Shorter proof of abf 4122 (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 33227 | . 2 ⊢ (∀𝑥 ¬ 𝜑 → {𝑥 ∣ 𝜑} = ∅) | |
2 | bj-abf.1 | . 2 ⊢ ¬ 𝜑 | |
3 | 1, 2 | mpg 1872 | 1 ⊢ {𝑥 ∣ 𝜑} = ∅ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 = wceq 1631 {cab 2757 ∅c0 4063 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-v 3353 df-dif 3726 df-nul 4064 |
This theorem is referenced by: (None) |
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