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Mirrors > Home > MPE Home > Th. List > eq0f | Structured version Visualization version Unicode version |
Description: The empty set has no elements. Theorem 2 of [Suppes] p. 22. (Contributed by BJ, 15-Jul-2021.) |
Ref | Expression |
---|---|
eq0f.1 |
Ref | Expression |
---|---|
eq0f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eq0f.1 | . . 3 | |
2 | nfcv 2764 | . . 3 | |
3 | 1, 2 | cleqf 2790 | . 2 |
4 | noel 3919 | . . . 4 | |
5 | 4 | nbn 362 | . . 3 |
6 | 5 | albii 1747 | . 2 |
7 | 3, 6 | bitr4i 267 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wal 1481 wceq 1483 wcel 1990 wnfc 2751 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: neq0f 3926 eq0 3929 ab0 3951 bnj1476 30917 stoweidlem34 40251 |
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