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Mirrors > Home > MPE Home > Th. List > dmopab | Structured version Visualization version Unicode version |
Description: The domain of a class of ordered pairs. (Contributed by NM, 16-May-1995.) (Revised by Mario Carneiro, 4-Dec-2016.) |
Ref | Expression |
---|---|
dmopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfopab1 4719 | . . 3 | |
2 | nfopab2 4720 | . . 3 | |
3 | 1, 2 | dfdmf 5317 | . 2 |
4 | df-br 4654 | . . . . 5 | |
5 | opabid 4982 | . . . . 5 | |
6 | 4, 5 | bitri 264 | . . . 4 |
7 | 6 | exbii 1774 | . . 3 |
8 | 7 | abbii 2739 | . 2 |
9 | 3, 8 | eqtri 2644 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 wex 1704 wcel 1990 cab 2608 cop 4183 class class class wbr 4653 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-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: dmopabss 5336 dmopab3 5337 mptfnf 6015 opabiotadm 6260 fndmin 6324 dmoprab 6741 zfrep6 7134 hartogslem1 8447 rankf 8657 dfac3 8944 axdc2lem 9270 shftdm 13811 dfiso2 16432 adjeu 28748 |
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