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Mirrors > Home > MPE Home > Th. List > dmopab3 | Structured version Visualization version Unicode version |
Description: The domain of a restricted class of ordered pairs. (Contributed by NM, 31-Jan-2004.) |
Ref | Expression |
---|---|
dmopab3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2917 | . 2 | |
2 | pm4.71 662 | . . 3 | |
3 | 2 | albii 1747 | . 2 |
4 | dmopab 5335 | . . . . 5 | |
5 | 19.42v 1918 | . . . . . 6 | |
6 | 5 | abbii 2739 | . . . . 5 |
7 | 4, 6 | eqtri 2644 | . . . 4 |
8 | 7 | eqeq1i 2627 | . . 3 |
9 | eqcom 2629 | . . 3 | |
10 | abeq2 2732 | . . 3 | |
11 | 8, 9, 10 | 3bitr2ri 289 | . 2 |
12 | 1, 3, 11 | 3bitri 286 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 cab 2608 wral 2912 copab 4712 cdm 5114 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-dm 5124 |
This theorem is referenced by: dmxp 5344 fnopabg 6017 opabn1stprc 7228 n0el2 34103 |
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