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Mirrors > Home > MPE Home > Th. List > dfnul3 | Structured version Visualization version Unicode version |
Description: Alternate definition of the empty set. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
dfnul3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 926 | . . . . 5 | |
2 | equid 1939 | . . . . 5 | |
3 | 1, 2 | 2th 254 | . . . 4 |
4 | 3 | con1bii 346 | . . 3 |
5 | 4 | abbii 2739 | . 2 |
6 | dfnul2 3917 | . 2 | |
7 | df-rab 2921 | . 2 | |
8 | 5, 6, 7 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wa 384 wceq 1483 wcel 1990 cab 2608 crab 2916 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-rab 2921 df-v 3202 df-dif 3577 df-nul 3916 |
This theorem is referenced by: difidALT 3949 kmlem3 8974 |
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