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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ab0 | Structured version Visualization version Unicode version |
Description: The class of sets verifying a falsity is the empty set (closed form of abf 3978). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-ab0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1839 | . . 3 | |
2 | bj-stdpc4v 32754 | . . . . 5 | |
3 | sbn 2391 | . . . . 5 | |
4 | 2, 3 | sylib 208 | . . . 4 |
5 | df-clab 2609 | . . . 4 | |
6 | 4, 5 | sylnibr 319 | . . 3 |
7 | 1, 6 | alrimih 1751 | . 2 |
8 | eq0 3929 | . 2 | |
9 | 7, 8 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wal 1481 wceq 1483 wsb 1880 wcel 1990 cab 2608 c0 3915 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-dif 3577 df-nul 3916 |
This theorem is referenced by: bj-abf 32903 bj-csbprc 32904 |
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